How To Do A Square Root

Calculating a square root means finding the number that multiplied by itself, that is, raising it to the square gives us the original number as a result.

If the number is a quadratic number, the square root is exact, working with the natural numbers, that is, the integers and positive numbers.

If we say that 6 × 6 = 6 ² = 36 then the square root of 36 is 6, another example: If 4 × 4 is 16 = 4 ² = 16 then the square root of 16 is 4

Calculating square roots is easy if you understand the concept: finding the square root of a number means finding that number that squared (multiplied by itself) gives you the number you started from.

There are numbers whose square root is exact, whether within natural numbers, integers, decimals or fractions, but there are others that are not exact and for this you have to make a special algorithm to be accurate or do it by approximation, depending on your need. Numbers whose square roots are exact are called quadratic numbers.

The quadratic numbers come from raising each number to the square, that is, multiplying them by themselves. For example, the square root of 49 is 7 because 7 × 7 is 49. This is written:

There are approximate methods to calculate the non-exact roots, these can be replaced by calculators and avoid cumbersome work which we will explain so that you know them in case you have to calculate a square root and you do not have access to a calculator.

At Doncomos.com we will give you the procedure so that you know how to do a square root without a calculator, but we will also teach you how to approximate, depending on the need.

What do you need to make a square root?

• Paper, pencil
• Calculator

Instructions for making a square root

1. To calculate a square root we must first know the parts of it: the number that is inside the root symbol (81) is called the radicand, the small number that is on top of the symbol is called the index (in this case it is a 2 and although I wrote it, remember that when it is a two, it is not written ) and the result is called the square root(9).
2. Example:
3. We will work first with the quadratic numbers and since these are easy to remember square roots we will mae a list:
4. These square roots are easy to calculate if we remember the squares of the main numbers, say from zero to 10, 11 or 12 and also some simple numbers like 20, 30, 40… as well as 100 or 10,000 or 100,000, etc.
5. The more we know, the easier it will be, there are easy multiplications that allow us to calculate easy roots, for example if 20 x 20 is 400, the square root of 400 will be 20. Look at this detail: when you multiply 20 x 20 you are multiplying 2×2= 4 and you are adding a zero from each number 20, then you will have: 20 x 20 = 400, therefore the square root of 400 can be divided into two parts: we calculate the root of 4 (which is 2) and as 4 00 has two zeros to the two we add a single zero to the right, that is, we divide the number of zeros by two (this is when it is a square root, if it were a cube root they are divided by three). Remember this procedure can be applied when the number is quadratic, if instead we had 500 and we wanted to take the square root this would not work for us because 5 does not have an exact square root, it would be 26.067977…..(we could approximate it to 26.07) but for this case we should resort to a calculator or to the algorithm that we will explain to you.
6. But if we want to calculate a square root that is not exact we can do it by approximation, for example if we want to calculate the square root of 30 it will not be an integer but at least we can know which numbers it will be between. What are the nearest square numbers? By default it is 25 and by excess it is 36, therefore the square root of 30 will be between 5 and 6, that is, it will be a little larger than 5 but less than 6. If we solve it with a calculator to verify we will see that: √30= 5.47…
7. Now we will calculate the square root of a larger number to learn the algorithm: For example: If we want to find the square root of 131137, the first thing we must do is separate the digits two by two from right to left as shown in the figure. We draw some lines that will be used for calculations, the first is where we will form the result of the square root.
8. We take the first number, which in this case is two digits (13) and look for which number multiplied by itself is close, without going over to 13. We write it to the right: 3×3=9 and we place that result below 13 and we subtract (13-9=4). In the upper part we put the first digit of the result, which is 3.
9. Now we lower the following two digits, forming the number 411. In the second space we place double 3 (3×2=6), that is, the first digit of the result.
10. In the next step we must add a number behind the 6 that will be the second digit of the number that will form with the 6 and we will multiply it by also by it without exceeding 411 and being as close as possible, for example: 62×2= 124(is very far from 411, 66 x 6=396, this is the correct one because if we do 67×7 we will go too far. We write it and place 6 as the second digit of the result . We subtract 411-396= 15.
11. In the next step we lower the following two digits forming the number 1537. We write twice 36 which is 72 and again we look for a number to add after 72 and that when multiplied does not exceed 1537. For example: 723 x 3= 2169 ( it goes through what we will look for smaller). If you try you will see that the only possibility is 2 because 72 2x 2 = 1444, then we put it under 1537 and subtract. We add the 2 in the final result (362) and we are left with a remainder of 93.

Tips for making a square root

• Remember that in a square root the index is not written but it is understood that it is “2”, in the others they are written, for example in the cube root there is a 3 in the fourth root there is a 4, etc, the only one that does not is written is 2.
• If you have to take the square root of a number with decimals, you must first separate the integer part by twos from the comma from right to left and the decimal part by twos from left to right.
• Find easy solutions to math problems in our specific category for this subject.