How to calculate the square root of 100. Square root

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, do not look 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's accession to 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 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 University for the Humanities, 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 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 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. Into which, by the way, he was again driven 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 been the head of 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 matters 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 at once: a 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 government 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 taking 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 solve the problem of higher education by closing and merging universities, they actually signed their own verdict. They didn't even bother to think about what kind of deep forces they raise. And this will end tragically, not only for those who are today 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 RGTEU only at first glance look like a kind of "trade revolution". In fact, they are the harbingers of another - 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, today's 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.

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 to study 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 hundred (100x100 \u003d 10000). If in the number under the square. with a 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 a square root is called a radical and looks like this.

And the square root of 100 is easy to get 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 know this either, 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 up; 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 has been ingrained in memory for a lifetime. The number 100 is obtained by multiplying 10 by 10, and therefore the number 10 and will be the root of a hundred.

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 did you have to take roots out of your life, except in the country? For example, such an entertaining task, like the square root of 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! An hour or two does not have time to pass, as can be calculated, using the well-known method of multiplication in "column", any square root. If you have the skills, a couple of minutes are 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 corrected 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 a "fork" 100 and 120. Let's choose 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 continue or stop 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 the extraction of 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 "The Guide to Algebra".

What is square root?

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For those who are "not very ..."
And for those who are "very even ...")

This concept is very simple. Natural, I would say. Mathematicians try to find a reaction for every action. There is addition - there is also subtraction. There is multiplication - there is also division. There is a squaring ... So there is also extraction of the square root! That's all. This action ( square root extraction) in mathematics is indicated by this icon:

The icon itself is called a beautiful word " radical".

How do you extract the root? It is better to look at examples.

What is the square root of 9? What number squared will give us 9? 3 squared gives us 9! Those:

But how much is the square root of zero? No problem! What number squared gives zero? Yes itself gives zero! Means:

Have caught what is square root? Then we consider examples:

Answers (in disarray): 6; 1; 4; nine; five.

Have you decided? Indeed, it’s much easier ?!

But ... What does a person do when he sees a task with roots?

Man begins to yearn ... He does not believe in the simplicity and lightness of the roots. Although, it seems, he knows what is square root...

This is because the person ignored several important points when studying roots. Then these little fads take cruel revenge on tests and exams ...

The first point. The roots must be recognized by sight!

How much is the square root of 49? Seven? Right! How did you know that seven? Squared 7 and got 49? Right! Please note that extract root out of 49 we had to do the reverse operation - to square 7! And make sure we don't miss. Or they could have missed ...

This is the difficulty extraction of roots. Square any number can be done without too much trouble. To multiply the number by itself in a column - and that's all. But for extracting the root there is no such simple and trouble-free technology. Has to pick up answer and check it for squaring.

This complex creative process - choosing the answer - is greatly simplified if you remember squares of popular numbers. Like a multiplication table. If, say, you need to multiply 4 by 6 - you don't add 4 6 times, do you? The answer immediately comes up 24. Although, not all of them come up with it, yes ...

For free and successful work with roots, it is enough to know the squares of numbers from 1 to 20. Moreover there and back. Those. you should easily name both, say, 11 squared and the square root of 121. There are two ways to achieve this memorization. The first is to learn the table of squares. This is great for solving examples. The second is to solve more examples. This will greatly help you remember the table of squares.

And no calculators! For verification only. Otherwise, you will mercilessly slow down the exam ...

So, what is square root And How root out - I think it's understandable. Now let's find out FROM WHAT you can extract them.

The second point. Root, I don't know you!

What numbers can you get square roots from? Yes, almost any. It's easier to understand from what can't retrieve them.

Let's try to calculate the following root:

To do this, you need to choose a number that squared will give us -4. We select.

What, is not selected? 2 2 gives +4. (-2) 2 gives +4 again! That's it ... There are no numbers that, when squared, will give us a negative number! Although I know such numbers. But I won't tell you). Go to college - you will find out for yourself.

The same story will be with any negative number. Hence the conclusion:

An expression in which the square root sign is a negative number - makes no sense! This is a forbidden operation. As forbidden as division by zero. Remember this fact ironically! Or, in other words:

You cannot extract square roots from negative numbers!

But from all the others - you can. For example, it is quite possible to calculate

At first glance, this is very difficult. Pick up fractions, but square them ... Don't worry. When we deal with the properties of the roots, such examples will be reduced to the same table of squares. Life will become easier!

Well, okay fractions. But we still come across expressions like:

Nothing wrong. All the same. The square root of two is the number that, when squared, will give us two. Only the number is completely uneven ... Here it is:

Interestingly, this fraction never ends ... Such numbers are called irrational. In square roots, this is the most common thing. By the way, this is why expressions with roots are called irrational... It is clear that it is inconvenient to write such an infinite fraction all the time. Therefore, instead of an infinite fraction, they leave it like this:

If, while solving the example, you end up with something unrecoverable, such as:

then we leave it that way. This will be the answer.

It is necessary to clearly understand that under the icons

Of course, if the root of the number is extracted smooth, you must do it. Task response in the form, for example

quite a complete answer.

And, of course, you need to know the approximate values \u200b\u200bby heart:

This knowledge helps a lot to assess the situation in difficult tasks.

The third point. The most cunning.

The main confusion in working with roots is brought in by this point. It is he who gives the lack of confidence in their own abilities ... Let's deal with this fad properly!

To begin with, let's take the square root of four of them again. What, have I already got you with this root?) Nothing, now it will be interesting!

What is the number squared 4? Well, two, two - I hear disgruntled answers ...

Right. Two. But after all minus two will give in square 4 ... And meanwhile, the answer

correct, and the answer

gross mistake. Like this.

So what's the deal?

Indeed, (-2) 2 \u003d 4. And under the definition of a square root of four minus two is quite suitable ... This is also the square root of four.

But! In the school course of mathematics, it is customary to count as square roots only non-negative numbers! Ie zero and all positive. Even a special term was coined: from the number and - this is non-negative number whose square is and... Negative results when extracting the arithmetic square root are simply discarded. At school, all square roots are arithmetic... Although not specifically mentioned.

Okay, that's understandable. It's even better not to bother with negative results ... This is not confusion yet.

The confusion starts when solving quadratic equations. For example, you need to solve the following equation.

The equation is simple, we write the answer (as taught):

This answer (absolutely correct, by the way) is just an abbreviated notation two answers:

Stop stop! A little higher I wrote that the square root is a number is always non-negative! And here is one of the answers - negative! Disorder. This is the first (but not the last) problem that causes distrust of the roots ... Let's solve this problem. Let's write the answers (purely for understanding!) Like this:

The parentheses do not change the essence of the answer. I just separated with parentheses signs from root... Now you can clearly see that the root itself (in brackets) is still a non-negative number! And the signs are the result of solving the equation... After all, when solving any equation, we must write all x, which, when substituted into the original equation, will give the correct result. Our equation fits the root of five (positive!) With both plus and minus.

Like this. If you just extract the square root out of anything, you is always get one non-negative result. For example:

Because it - arithmetic square root.

But if you are solving some kind of quadratic equation like:

then is always turns out two answer (with plus and minus):

Because it's the solution to the equation.

Hopefully what is square root with your little points you figured it out. Now it remains to find out what can be done with the roots, what are their properties. And what are the faddles and underwater crust ... sorry, stones!)

All this is in the following lessons.

If you like this site ...

By the way, I have a couple more interesting sites for you.)

You can practice solving examples and find out your level. Instant validation testing. Learning - with interest!)

you can get acquainted with functions and derivatives.

Today we will figure out on this page of our website the site about how much the square root of 100 will be. Let's figure out together with you how much the square root of 100 will be, since 1000 researchers have been racking their minds over this topic for many decades, and many have come to the conclusion that such a root does not exist at all and it is simply impossible to calculate it. It is also very important in this case to ask exactly the right question to identify the square root of 100. To be precise, we will calculate the arithmetic root of the square of 100, since in the usual square root of 100, as a result, we will get two numbers: 10 and - ten.

We can calculate the sum of these numbers we need with a simple arithmetic trick using a vertical, familiar line, numbers and roots that are written on the bottom right. There we will find the square of units of the root we need, then multiply tens and find the doubled, not triple, product of ten of any root by units. We will have to square some numbers so that the total is a two-digit number, if in the end we got the number 10, then we did everything right with you. The main thing is, initially, before starting the calculations, at least a little to make friends with mathematics and with a mathematical progression, drawing up a square root.

Remember one single and basic rule: in order for us to extract the required square root of any integer, first of all, we extract any root we need from the number of its sums and hundreds. If the number is equal to or greater than 100, then we start looking for the root of hundreds of actual numbers of these hundreds, then of tens of thousands of the actual number, especially if the given number is much more than 100, then without fail we extract the root of the number from hundreds of tens of thousands or to be more precise: out of a million of a given number. There are many rules and various scientific recommendations on this topic, school programs for extracting the square root of the number 100 will always be the same.

If we consider the progress of finding the root of the number 100, we need to note that there are as many digits in the root as there are under a finite number of faces, while the left side can consist of only one digit. Based on all this, the most accurate square root of any number on the planet earth will be called such a sum of numbers, the square of which is exactly equal to the given number when calculating. It is on this that we can end our short course on calculating the square root of 100, which will equal (10) ten.

Konstantinova Vera

How to find the root of a number

The problem of finding a root in mathematics is the inverse problem of raising a number to a power. There are different roots: roots of the second degree, roots of the third degree, roots of the fourth degree, and so on. It depends on the degree to which the number was originally raised. The root is denoted by the symbol: √ is the square root, that is, the root of the second degree, if the root has a degree greater than the second, then the corresponding degree is assigned above the root sign. The number under the root sign is a radical expression. When finding a root, there are several rules that will help you not to be mistaken in finding a root:

• An even root (if the degree is 2, 4, 6, 8, etc.) of a negative number does NOT exist. If the radical expression is negative, but an odd root is searched for (3, 5, 7, and so on), then the result will be negative.
• The root of any power of one is always one: √1 \u003d 1.
• The root of zero is zero: √0 \u003d 0.

Find the root of 100

If the problem does not say the root of what degree must be found, then it is usually implied that it is necessary to find the root of the second degree (square).
Find √100 \u003d? We need to find a number that, when raised to the second power, will give the number 100. Obviously, this number is the number 10, since: 10 2 \u003d 100. Therefore, √100 \u003d 10: the square root of 100 is 10.