# How to extract the root?

In mathematics, the question of how to extract a root is considered relatively simple. If we square the numbers from the natural series: 1, 2, 3, 4, 5 ... n, then we get the following row of squares: 1, 4, 9, 16 ... n2. The number of squares is infinite, and if you look at it carefully, you will see that there are not so many integers in it. Why this is so, we will explain a little later.

## Number root: calculation rules and examples

So, we have built the number 2 in the square, that is, multiplied it by itself and got 4. And how to extract the root from the number 4? At once we say that the roots can be square, cubic, and of any degree to infinity.

The degree of the root is always a natural number, that is, it is impossible to solve such an equation: a root of 3.6 from n.

### Square root

Let us return to the question of how to extract the square root of 4. Since we built the number 2 exactly in the square, then we will also extract the square root. In order to correctly extract the root of 4, you just need to choose the right number, which, when squared, would give the number 4. And this, of course, 2. Look at an example:

- 22=4
- The root of 4 = 2

This example is pretty simple. Let's try to extract the square root of 64. What is the number, when multiplying by itself, is 64? Obviously, this is 8.

- 82=64
- The root of 64 = 8

### Cubic root

As mentioned above, the roots are not only square, using an example we will try to more clearly explain how to extract a cube root or a root of the third degree. The principle of extracting a cubic root is the same as that of a square root, the only difference is that the desired number was initially multiplied by itself not once, but twice. That is, let's say we took the following example:

- 3x3x3 = 27
- Naturally, the cube root of 27 will be a triple:
- Root3out of 27 = 3

Suppose it is necessary to find the cubic root of 64. To solve this equation, it suffices to find a number that, if raised to a third power, would give 64.

- 43=64
- Root3out of 64 = 4

### Extract root from number on calculator

Of course, it’s best to learn how to extract square, cubic and roots of another degree in practice by solving many examples and memorizing a table of squares and cubes of small numbers. In the future, this will greatly facilitate and shorten the time to solve equations. Although, it should be notedthat sometimes it is necessary to extract a root from such a large number that it will cost a lot of hard work to find the right number squared, if at all possible. To help in extracting the square root will come the usual calculator. How to extract the root on the calculator? Very simply enter the number from which you want to find the result. Now carefully look at the buttons of the calculator. Even on the simplest of them there is a key with a root icon. By clicking on it, you will immediately get the finished result.

Not every number can extract a whole root, consider the following example:

The root of 1859 = 43,116122 ...

You can try to solve this example in parallel on a calculator. As you can see, the resulting number is not an integer, moreover, the set of numbers after the comma is not finite. Special engineering calculators can give a more accurate result, but on the display of ordinary ones, the full result simply does not fit. And if you continue the series of squares begun earlier, you will not find the number 1859 in it just because the number that was squared to get it is not an integer.

If you need to extract the third degree root on a simple calculator, then you must double-click on the button with the root sign.For example, take the number 1859 used above and extract the cube root from it:

Root3from 1859 = 6,5662867 ...

That is, if the number 6.5662867 ... is raised to a third power, then we will get approximately 1859. Thus, it is not difficult to extract the roots from numbers, just remember the above algorithms.

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