Multiple root of 100. What is square root? Bitwise calculation of the square root value

Before the advent of calculators, students and teachers used to calculate square roots by hand. There are several ways to manually calculate the square root of a number. Some of them offer only an approximate solution, others provide a precise answer.

Steps

Prime factorization

Factor the radical number that is square. Depending on the root number, you will get an approximate or exact answer. Square numbers are numbers from which you can extract a whole square root. Multipliers are numbers that, when multiplied, give the original number. For example, the factors of 8 are 2 and 4, since 2 x 4 \u003d 8, 25, 36, 49 are square numbers, since √25 \u003d 5, √36 \u003d 6, √49 \u003d 7. Square factors are factors which are square numbers. First, try to square the root number.

• For example, calculate the square root of 400 (manually). Try to square 400 first. 400 is a multiple of 100, which is divisible by 25, which is a square number. If you divide 400 by 25, you get 16. 16 is also a square number. Thus, 400 can be factored into square factors of 25 and 16, that is, 25 x 16 \u003d 400.
• It can be written as follows: √400 \u003d √ (25 x 16).

1. The square root of the product of some terms is equal to the product of the square roots of each term, that is, √ (a x b) \u003d √a x √b. Use this rule and take the square root of each square factor and multiply the results to find your answer.

   • In our example, extract the root of 25 and 16.
     • √ (25 x 16)
     • √25 x √16
     • 5 x 4 \u003d 20

2. If the radical number does not expand into two square factors (and this happens in most cases), you will not be able to find the exact answer in the form of an integer. But you can simplify the problem by factoring the root number into a square factor and an ordinary factor (a number from which the whole square root cannot be extracted). Then you will take the square root of the square factor and you will take the root of the ordinary factor.

   • For example, calculate the square root of 147. The number 147 cannot be factored into two square factors, but it can be factored into the following factors: 49 and 3. Solve the problem as follows:
     • \u003d √ (49 x 3)
     • \u003d √49 x √3
     • = 7√3

3. Estimate the root value if needed. Now you can estimate the value of the root (find an approximate value) by comparing it with the values \u200b\u200bof the roots of the square numbers that are closest (on both sides on the number line) to the root number. You will get the root value as a decimal fraction, which must be multiplied by the number behind the root sign.

   • Let's go back to our example. The radical number 3. The nearest square numbers to it will be the numbers 1 (√1 \u003d 1) and 4 (√4 \u003d 2). So √3 is between 1 and 2. Since √3 is probably closer to 2 than 1, our estimate is √3 \u003d 1.7. We multiply this value by the number at the root sign: 7 x 1.7 \u003d 11.9. If you do the calculations on a calculator, you get 12.13, which is pretty close to our answer.
     • This method also works with large numbers. For example, consider √35. The root number is 35. The nearest square numbers to it will be the numbers 25 (√25 \u003d 5) and 36 (√36 \u003d 6). So √35 is between 5 and 6. Since √35 is much closer to 6 than to 5 (because 35 is only 1 less than 36), we can say that √35 is slightly less than 6. Checking on a calculator gives us an answer of 5.92 - we were right.

4. Another way is factor the radical number into prime factors . Prime factors are numbers that are divisible only by 1 and themselves. Write down the prime factors in a row and find pairs of the same factors. Such factors can be taken out beyond the root sign.

   • For example, calculate the square root of 45. We decompose the radical number into prime factors: 45 \u003d 9 x 5, and 9 \u003d 3 x 3. Thus, √45 \u003d √ (3 x 3 x 5). 3 can be taken outside the root sign: √45 \u003d 3√5. Now you can estimate √5.
   • Consider another example: √88.
     • \u003d √ (2 x 44)
     • \u003d √ (2 x 4 x 11)
     • \u003d √ (2 x 2 x 2 x 11). You got three multipliers of 2; take a couple of them and place them outside the root sign.
     • \u003d 2√ (2 x 11) \u003d 2√2 x √11. Now you can evaluate √2 and √11 and find a rough answer.

   Calculating the square root manually

   Long division

   1. This method involves a process similar to long division and gives the exact answer. First, draw a vertical line dividing the sheet into two halves, and then draw a horizontal line to the right and slightly below the top edge of the sheet to the vertical line. Now divide the radicalized number into pairs of numbers, starting with the fractional part after the decimal point. So, the number 79520789182.47897 is written as "7 95 20 78 91 82, 47 89 70".

      • As an example, let's calculate the square root of 780.14. Draw two lines (as shown in the picture) and on the top left write this number as "7 80, 14". It is normal that the first digit on the left is an unpaired digit. The answer (the root of the given number) will be written in the upper right.

   2. For the first pair of numbers (or one number) on the left, find the largest integer n whose square is less than or equal to the pair of numbers (or one number) in question. In other words, find the square number that is closest to but less than the first pair of numbers (or one number) on the left, and extract the square root of that square number; you get the number n. Write the found n in the upper right, and the square n in the lower right.

      • In our case, the first number on the left will be 7. Next, 4< 7, то есть 2 2 < 7 и n = 2. Напишите 2 сверху справа - это первая цифра в искомом квадратном корне. Напишите 2×2=4 справа снизу; вам понадобится это число для последующих вычислений.

   3. Subtract the square of the number n you just found from the first pair of numbers on the left (or one number). Write down the calculation result under the subtracted (the square of the number n).

      • In our example, subtract 4 from 7 to get 3.

   4. Pull down the second pair of numbers and write it down near the value obtained in the previous step. Then double the number at the top right and write your result at the bottom right with "_ × _ \u003d" added.

      • In our example, the second pair of numbers is "80". Write "80" after 3. Then, double the number at the top right gives 4. Write "4_ × _ \u003d" at the bottom right.

   5. Fill in the dashes on the right.

      • In our case, if instead of dashes we put the number 8, then 48 x 8 \u003d 384, which is more than 380. Therefore, 8 is too large a number, but 7 will do. Write 7 instead of dashes and get: 47 x 7 \u003d 329. Write 7 from the top right - this is the second digit in the required square root of 780.14.

   6. Subtract the resulting number from the current number on the left. Record the result from the previous step under the current number on the left, find the difference and write it down under the subtracted one.

      • In our example, subtract 329 from 380, which is 51.

   7. Repeat step 4. If the demolished pair of numbers is the fractional part of the original number, then put the separator (comma) of the integer and fractional parts in the desired square root from the top right. On the left, drag down the next pair of numbers. Double the number at the top right and write your result at the bottom right with "_ × _ \u003d" added.

      • In our example, the next pair of numbers to be demolished will be the fractional part of 780.14, so put the separator of the integer and fractional parts in the desired square root in the top right. Take down 14 and write down on the bottom left. The doubled number on the top right (27) is 54, so write "54_ × _ \u003d" on the bottom right.

   8. Repeat steps 5 and 6. Find such the largest number in place of the dashes on the right (instead of dashes, you need to substitute the same number) so that the multiplication result is less than or equal to the current number on the left.

      • In our example, 549 x 9 \u003d 4941, which is less than the current number on the left (5114). Write 9 on the top right and subtract the multiplication from the current number on the left: 5114 - 4941 \u003d 173.

   9. If you need to find more decimal places for the square root, write a couple of zeros next to the current number on the left and repeat steps 4, 5 and 6. Repeat the steps until you get the precision you want (the number of decimal places).

   Understanding the process

   To master this method, imagine the number whose square root you want to find as the area of \u200b\u200ba square S. In this case, you will look for the length of the side L of such a square. We calculate the value of L for which L² \u003d S.

   Give a letter for each digit in the answer. We denote by A the first digit in the value of L (the required square root). B will be the second digit, C the third, and so on.

   Specify a letter for each pair of leading digits. Let's denote by S a the first pair of digits in the value of S, by S b - the second pair of digits, and so on.

   Understand the relationship of this method to long division. As in the division operation, where each time we are interested in only one next digit of the dividend, when calculating the square root, we work sequentially with a pair of digits (to get one next digit in the value of the square root).

   1. Consider the first pair of digits Sa of the number S (Sa \u003d 7 in our example) and find its square root. In this case, the first digit A of the required value of the square root will be such a digit, the square of which is less than or equal to S a (that is, we are looking for an A such that the inequality A² ≤ Sa< (A+1)²). В нашем примере, S1 = 7, и 2² ≤ 7 < 3²; таким образом A = 2.

      • Let's say you want to divide 88962 by 7; here the first step will be similar: we consider the first digit of the divisible number 88962 (8) and select the largest number that, when multiplied by 7, gives a value less than or equal to 8. That is, we are looking for a number d for which the inequality is true: 7 × d ≤ 8< 7×(d+1). В этом случае d будет равно 1.

Among the many knowledge that is a sign of literacy, the alphabet is in the first place. The next, the same "sign" element, are the skills of addition-multiplication and, adjacent to them, but inverse in meaning, arithmetic subtraction-division operations. The skills learned in distant school childhood serve faithfully day and night: TV, newspaper, SMS, and everywhere we read, write, count, add, subtract, multiply. And, tell me, how often have you had to extract roots in life, except in the country? For example, such an entertaining task, like the square root of the number 12345 ... Is there still gunpowder in the flasks? Will we master? Nothing could be easier! Where is my calculator ... And without it, hand-to-hand, weak?

First, let's clarify what it is - the square root of a number. Generally speaking, “to take a root from a number” means to perform an arithmetic operation opposite to raising to a power - here you have the unity of opposites in life's application. let's say a square is a multiplication of a number by itself, ie, as taught in school, X * X \u003d A or in another notation X2 \u003d A, and in words - "X squared equals A". Then the inverse problem sounds like this: the square root of the number A, is the number X, which, when squared is equal to A.

Extracting the square root

From the school course of arithmetic, methods of calculations "in a column" are known, which help to perform any calculations using the first four arithmetic operations. Alas ... For square, and not only square, roots of such algorithms do not exist. So how do you get the square root without a calculator? Based on the definition of the square root, there is only one conclusion - it is necessary to select the value of the result by sequential enumeration of numbers, the square of which approaches the value of the radical expression. That's all! Before an hour or two has passed, how can you calculate any square root using the well-known method of multiplication in a "column". If you have the skills, a couple of minutes is enough for this. Even a not quite advanced calculator or PC user does it in one fell swoop - progress.

But seriously, the calculation of the square root is often performed using the "artillery fork" technique: first, they take a number whose square approximately corresponds to the radical expression. It is better if "our square" is slightly less than this expression. Then the number is adjusted according to their own skill-understanding, for example, multiplied by two, and ... again squared. If the result is greater than the number under the root, successively adjusting the original number, gradually approach its "colleague" under the root. As you can see, there is no calculator, only the ability to count "in a column". Of course, there are many scientifically argued and optimized algorithms for calculating the square root, but for "home use" the above technique gives 100% confidence in the result.

Yes, I almost forgot, to confirm our increased literacy, let's calculate the square root of the previously indicated number 12345. We do it step by step:

1. Take, purely intuitively, X \u003d 100. Let's count: X * X \u003d 10000. Intuition is on top - the result is less than 12345.

2. Let's try, also purely intuitively, X \u003d 120. Then: X * X \u003d 14400. And again with intuition the order - the result is more than 12345.

3. Above we got the "fork" 100 and 120. Let's choose the new numbers - 110 and 115. We get, respectively, 12100 and 13225 - the fork is narrowing.

4. Trying "at random" X \u003d 111. We get X * X \u003d 12321. This number is already close enough to 12345. In accordance with the required accuracy, "fitting" can be continued or stopped at the result. That's all. As promised - everything is very simple and without a calculator.

Just a little history ...

The Pythagoreans, pupils of the school and followers of Pythagoras, in 800 BC, thought of using square roots. and right there, "ran into" new discoveries in the field of numbers. And where did that come from?

1. Solving the problem with extracting the root, gives the result in the form of numbers of a new class. They were called irrational, in other words, "unreasonable", because they are not written with a complete number. The most classic example of this kind is the square root of 2. This case corresponds to the calculation of the diagonal of a square with side equal to 1 - here it is, the influence of the Pythagorean school. It turned out that in a triangle with a very specific unit size of the sides, the hypotenuse has a size that is expressed by a number that has "no end." This is how mathematics appeared

2. It is known that It turned out that this mathematical operation contains one more catch - when extracting the root, we do not know which number, positive or negative, the square of the radical expression is. This uncertainty, the double result from one operation, is recorded.

The study of problems associated with this phenomenon has become a direction in mathematics called the theory of a complex variable, which is of great practical importance in mathematical physics.

It is curious that the notation of the root - radical - was used in his "Universal Arithmetic" by the same ubiquitous I. Newton, and exactly the modern form of notation of the root has been known since 1690 from the book of the Frenchman Rolle "Guide to Algebra".

Well, if we consider that this very square root is the product of the same number (that is, b \u003d a), then the square root of a hundred will be 10 (100 \u003d 10).

It should be noted that you can represent the number 100 as the product of 25 and 4. And then calculate the square root of both 25 and 4. 5 and 2. Multiply and get also 10.

When we first started studying this topic at school, square root of 100was probably one of the easiest to understand and calculations... Usually I looked at an even (!) Number of zeros and immediately calculated what number, multiplied by itself, gives the number under the square root. For example, if it were 10,000, then the square root of that number would be one hundred (100x100 \u003d 10000). If in the number under the square. by the root of six zeros, the answer will contain three zeros. Etc.

In this case, there are only two zeros in the figure, which means that there were two tens. So, the square root of 100 is 10. We check: 10x10 \u003d 100

There are several ways to calculate the square root.

1) Take a calculator or smartphone / tablet / computer with the installed program for calculations, enter the number 100 and click on the square root icon, which looks something like this:

2) Know the table of squares of numbers up to 100 \u003d 25 * 4.

3) By the method of division.

4) By the method of decomposition into prime factors 100 \u003d 10 * 10.

Theoretically, if you do everything right, you will get a result equal to 10.

The icon that denotes the square root is called a radical and looks like this.

And the square root of 100 is easy to extract if you know the squares of the numbers. 10 X 10 \u003d 100. So the square root of 100, following the definition of a square root, is 10.

Probably every student knows that the number 100 is a product of 10 by 10.

Since the square root is a number that, when multiplied by itself, is a radical expression, then the square root of a hundred is 10.

If you forgot that 100 \u003d 10 * 10, then you can use the properties of the roots:

root of 100 \u003d root of (25 * 4) \u003d root of 25 * root of 4.

Everyone knows that 5 * 5 \u003d 25, and 2 * 2 \u003d 4. Therefore, the root of 100 \u003d 5 * 2 \u003d 10.

Well, if you don't even know this, then you can use a calculator or Excel tables, they have a special formula called ROOT... This is how it looks visually:



Nowadays, using a calculator, it is very easy to calculate the square root of any number.

You can take the square root of the number 100 orally. After all, it is known that bringing the number x to the square is the number x multiplied by the number x.

If 10 10 \u003d 100, then the square root of 100 is 10.

Answer to the question: 10 .

The square root in mathematics is denoted by a conventional symbol.

The square root of a is a non-negative number whose square is a. Since 10 ^ 2 \u003d 100, the square root of 100 is 10.

There are numbers whose root is very easy to remember. For me, for example, 25 - the root will be 5, since 5 * 5 \u003d 25, 625 - the root of 25, since 25 * 25 \u003d 625.

I also include the number 100 among such numbers - the root will be 10, check 10 * 10 \u003d 100. So right.

The square root of a hundred? it looks like 10

I can hardly imagine that behind this answer a person will climb on the Internet, but if you imagine that he is completely `` unassembled and inattentive '', then I give the answer. The square root of the number 100 is equal to 10 ", as well as -10". In many sources it is written like this.



The square root of 100 has two meanings 10 and -10. Who does not believe can be checked by multiplication.

In order to extract the square root without a calculator, you need to resort to decomposing the number under the root into the smallest factors and start from there. So for the number one hundred:

And accordingly, from here it immediately becomes clear that the square root of a hundred will be exactly 10.

I had to remember a rule that I remember from school:

Although extracting a root from 100 is the simplest thing that does not require the use of calculators, since it is ingrained in memory for life. The number 100 is obtained by multiplying 10 by 10, and therefore the number 10 and will be the root of a hundred.

Quite often, when solving problems, we are faced with large numbers from which we need to extract square root... Many students decide that this is a mistake and begin to re-solve the whole example. In no case should you do this! There are two reasons for this:

1. Roots of large numbers do occur in problems. Especially in texting;
2. There is an algorithm by which these roots are counted almost orally.

We will consider this algorithm today. Perhaps some things will seem incomprehensible to you. But if you carefully consider this lesson, you will get the most powerful weapon against square roots.

So the algorithm:

1. Restrict the desired root from above and below to numbers that are multiples of 10. Thus, we will reduce the search range to 10 numbers;
2. From these 10 numbers, weed out those that definitely cannot be roots. As a result, there will be 1-2 numbers;
3. Square these 1-2 numbers. The one of them whose square is equal to the original number will be the root.

Before putting this algorithm into practice, let's take a look at each individual step.

Root restriction

First of all, we need to find out between which numbers our root is located. It is highly desirable that the numbers be divisible by ten:

10 2 = 100;
20 2 = 400;
30 2 = 900;
40 2 = 1600;
...
90 2 = 8100;
100 2 = 10 000.

We get a series of numbers:

100; 400; 900; 1600; 2500; 3600; 4900; 6400; 8100; 10 000.

What do these numbers give us? It's simple: we get boundaries. Take, for example, the number 1296. It lies between 900 and 1600. Therefore, its root cannot be less than 30 and more than 40:

[Figure caption]

The same is with any other number from which the square root can be found. For example 3364:

[Figure caption]

Thus, instead of an incomprehensible number, we get a very specific range in which the original root lies. To narrow down your search even further, move on to the second step.

Filtering out obviously extra numbers

So, we have 10 numbers - candidates for the root. We got them very quickly, without complicated thinking and long multiplications. It's time to move on.

Believe it or not, we will now reduce the number of candidate numbers to two - and again without any complicated calculations! It is enough to know a special rule. Here it is:

The last digit of the square depends only on the last digit original number.

In other words, just look at the last digit of the square and we will immediately understand where the original number ends.

There are only 10 digits that can come in last place. Let's try to figure out what they turn into when squared. Take a look at the table:

1	2	3	4	5	6	7	8	9	0
1	4	9	6	5	6	9	4	1	0

This table is another step towards calculating the root. As you can see, the numbers in the second line turned out to be symmetrical about the five. For instance:

2 2 = 4;
8 2 = 64 → 4.

As you can see, the last digit is the same in both cases. This means that, for example, the root of 3364 necessarily ends with 2 or 8. On the other hand, we remember the restriction from the previous paragraph. We get:

[Figure caption]

The red squares show that we do not know this figure yet. But the root lies in the range from 50 to 60, on which there are only two numbers ending in 2 and 8:

[Figure caption]

That's all! Of all the possible roots, we left only two options! And this is in the most difficult case, because the last digit can be 5 or 0. And then there will be only one candidate for roots!

Final calculations

So, we have 2 candidate numbers left. How do you know which one is the root? The answer is obvious: square both numbers. The one that squared gives the original number will be the root.

For example, for the number 3364, we found two candidate numbers: 52 and 58. Let's square them:

52 2 \u003d (50 +2) 2 \u003d 2500 + 2 · 50 · 2 + 4 \u003d 2704;
58 2 \u003d (60 - 2) 2 \u003d 3600 - 2 60 2 + 4 \u003d 3364.

That's all! It turned out that the root is 58! In this case, to simplify the calculations, I used the formula for the squares of the sum and difference. Thanks to which I didn't even have to multiply the numbers in a column! This is one more level of computational optimization, but, of course, it is completely optional :)

Examples of calculating roots

Theory is, of course, good. But let's put it to the test.

[Figure caption]

First, let's find out between which numbers the number 576 lies:

400 < 576 < 900
20 2 < 576 < 30 2

Now we look at the last figure. It is 6. When does this happen? Only if the root ends in 4 or 6. We get two numbers:

It remains to square each number and compare with the original:

24 2 = (20 + 4) 2 = 576

Excellent! The first square turned out to be equal to the original number. So this is the root.

Task. Calculate the square root:

[Figure caption]

900 < 1369 < 1600;
30 2 < 1369 < 40 2;

We look at the last figure:

1369 → 9;
33; 37.

Squaring:

33 2 \u003d (30 + 3) 2 \u003d 900 + 2 · 30 · 3 + 9 \u003d 1089 ≠ 1369;
37 2 \u003d (40 - 3) 2 \u003d 1600 - 2 · 40 · 3 + 9 \u003d 1369.

Here is the answer: 37.

Task. Calculate the square root:

[Figure caption]

We limit the number:

2500 < 2704 < 3600;
50 2 < 2704 < 60 2;

We look at the last figure:

2704 → 4;
52; 58.

Squaring:

52 2 \u003d (50 + 2) 2 \u003d 2500 + 2 · 50 · 2 + 4 \u003d 2704;

Received the answer: 52. The second number will not need to be squared.

Task. Calculate the square root:

[Figure caption]

We limit the number:

3600 < 4225 < 4900;
60 2 < 4225 < 70 2;

We look at the last figure:

4225 → 5;
65.

As you can see, after the second step, only one option remains: 65. This is the desired root. But let's still square it and check:

65 2 \u003d (60 + 5) 2 \u003d 3600 + 2 60 5 + 25 \u003d 4225;

Everything is correct. We write down the answer.

Conclusion

Alas, not better. Let's look at the reasons. There are two of them:

• On any normal exam in mathematics, be it the GIA or the Unified State Exam, the use of calculators is prohibited. And for carrying a calculator into the classroom, they can easily be kicked out of the exam.
• Don't be like stupid Americans. Which are not like roots - they cannot add two primes. And when they see fractions, they generally get hysterical.

"Trade" revolution
Komkov Sergey 26.12.2012

Against the background of Russia's just accession to the WTO, the destruction of RGTEU, the leading Russian university in the system of trade (and, first of all, foreign trade) relations, as well as the dismissal of its rector, well-known politician Sergei Baburin, look not just like stupidity. All this is very similar to a pre-planned provocation.

It seems that the World Trade Organization and, mainly, the United States, playing a key role in it, were seriously concerned about the possible consequences of Russia joining this organization.

But then they remembered in time that in Russia the organization, the Higher School of Economics, which they had grown and nurtured, had been successfully operating for a long time. It was she who was created in 1992 with the money of the World Bank with the aim of destroying the entire intellectual potential of the nation in our country. It is under her leadership that the main collective "agent of influence" in this area, the Ministry of Education and Science of Russia, operates today.

You can talk a lot and endlessly about the stupidity and incompetence of the newly minted minister, Mr. Livanov, who hardly distinguishes between the types and directions of education. But Mr. Livanov himself is absolute zero without a stick. From whose mouth, every time you open them, some next nonsense will certainly jump out. More colorful figures loom behind him. For example, the main "ideologist" of all economic transformations in our country, US citizen Yevgeny Yasin, and his henchman, HSE rector Yaroslav Kuzminov.

It was they who, at the suggestion of American advisers from the World Bank, who are actively working on the basis of the HSE, concocted the criteria for the so-called “monitoring” of Russian universities.

And it is no secret to anyone that, in accordance with these "criteria", the most significant Russian higher educational institutions have fallen into the category of "ineffective". Universities with a rich history and traditions, with great creative potential. For example, Moscow Architectural Institute, Russian State Humanitarian University, Literary Institute.

The Russian State Trade and Economic University - RGTEU also fell into this category. Although, according to many of its indicators, this university can give a hundred points of a handicap to the very "Pleshka", to which it was so suddenly decided to join. And, first of all, in matters of training specialists for the foreign trade system.

RGTEU does not just have huge international connections. It thoroughly studies the features of the trade development of foreign countries. Leading economic and political figures of the world, ambassadors of foreign states constantly appear within the walls of this university. The leading world leaders are honorary doctors of this university. For example, Fidel Castro and Hugo Chavez.

And these, as you know, are America's "sworn friends". So the tools were used to destroy such a dangerous educational institution. So that Russia, God forbid, does not turn off the "true path" and betray the interests of American customers.

And the personality of the rector himself - a well-known politician and scientist in Russia and far beyond its borders - has become like a bone in the throat of our American uncles.

Sergei Baburin was not just one of the leaders of the parliamentary opposition, occupying the place of vice-speaker in the previous composition of the State Duma of Russia. He was an active supporter of Russia's new policy throughout the post-Soviet space. It was he who in 2006 most actively helped the people of Abkhazia to get out of the deepest political crisis. In which, by the way, he was driven again by the same stupid and obedient to the will of American advisers, officials of the government and the presidential administration of Russia.

Thanks to the efforts of Sergei Baburin, progressive forces led by Sergei Bagapsh took the upper hand in Abkhazia. And since 2008, Abkhazia has become Russia's main strategic partner in the North Caucasus.

This position is an expression of sound, balanced patriotism. Therefore, for a number of years, Baburin has headed the Russian National Union and is the organizer of the annual traditional Russian Marches. Not those with a swastika and fascist slogans "Russia is only for Russians!" And statements, quite understandable for the entire population of the country, demanding to observe Russian national interests in foreign policy issues and to fulfill the social promises given to their own people.

But this is precisely what the American henchmen do not like, entrenched in the offices of the Russian government. Because for them the requirement to observe our national interests is like a knife to their hearts.

So it came to someone's mind to kill two birds with one stone: both the university that trains specialists for the successful foreign trade of Russia, and its patriotic rector.

Usually fools are best suited for this kind of action. For, as you know, they do not know what they are actually doing. But in this particular case, a very serious blunder may turn out, fraught with grave social consequences for the entire country.

Our officials, snickering at the state grub and considering themselves completely right in any unrighteous deed, have forgotten the simplest truth: they have no power over youthful souls and youthful impulses.

It was this kind of impulses that swept away the government of General De Gaulle in France at the end of the 60s of the last century. There, too, everything began with seemingly harmless things. It ended in general chaos, riots, burning cars and offices.

Youth (especially organized student youth) are not a bunch of bankrupt opposition politicians who have been in power and, therefore, are very offended at it. Student youth has always and at all times been one of the main driving forces of the revolution. And today's youth is no exception to the rule. Rather the opposite. It is today's youth, who are especially acutely aware of the social injustice and inequality that have arisen in society, who are capable of the steepest and most radical steps. And if the authorities try to use force, it will be fatal for them. Because young people will never forgive her for this.

When Mr. Livanov and Co. announced their intention to use force to begin solving the problem of higher education, closing and merging universities, they actually signed their own verdict. They didn't even bother to think about what deep forces they raise. And this will end tragically, not only for those who today are in leading positions in the Ministry of Education and Science, but for the entire Russian leadership as a whole. For even a locally suppressed youth rebellion does not go into oblivion. He is maturing with renewed vigor. But no one can predict where and when it will break out.

So the events at the RGTEU only at first glance look like a kind of "trade revolution". In fact, they are harbingers of another - a tougher and bloodier social war, in which there will be no winners.

The loser is known in advance. This is our homeland. A country that we still sometimes call with some pride Russia.

Therefore, the current actions of the leadership of the Ministry of Education and Science in relation to a separate educational institution and in relation to a separate rector can be regarded as inciting a social war in the name and for the benefit of another state.

And this is called: National Treason.