What is a SQUARE ROOT and how is it calculated?

Welcome to a teacher, in today's lesson we will see what is a square root and how to calculate it. We will explain important concepts first, then move on to see the process for calculating a square root. You will also find examples of the most common roots, so that you can review them whenever you want. Finally, you can find a exercise and its respective solution, so that you can verify that you have understood what was explained.

The square root is the opposite operation to empowerment. And in order to solve a power, what we do is multiply that number by itself, as many times as indicated by the exponent.

Index

1. What is a square root
2. How to calculate a square root - with examples
3. Square root exercises (with solutions)
4. Solutions

The square root of any number is that other number that multiplied by himselfor give that first number. In mathematics, we write it as the radical of index 2 or, alternatively, as a number raised to the power of one half (1/2).

Basically, the square root consists of find a number multiplied by itself or, put another way, a number raised to the square that gives the number that we have inside the radical. So, for example, we have to:

• √1 = 1
• √4 = 2
• √9 = 3
• √16 = 4
• √25 = 5
• √36 = 6
• √49 = 7
• √64 = 8
• √81 = 9
• √100 = 10

These are the most common square roots, So we recommend that you learn them by heart! They are the so-called square numbers, since there is an integer that, multiplied by itself, gives this first. Therefore, we can say that number 1 or number 49 are perfect square numbers.

Once we have seen what a square root is, we will move on to process to calculate it. To find the square root of a given number, we must find another number that if we multiply it by itself, the result is the radicand itselfor, that is, the first of the numbers that we had within the root.

For example: The square root of 64 is 8, since 8 x 8 = 64.

However, we are not always going to find the result by multiplying natural numbers by themselves, since sometimes the results are numbers with decimals. When this happens, what we will have to do is find the closest squared number to the initial of the filing, but without going over. That is, it will always be the smallest number between the two that are close.

Example: if we want to take the square root of 20, we see that 4 x 4 = 16 and 5 x 5 = 25, so what we will do is take the 4, since it is the closest one without going over.

Now is the time for you to practice what was explained in today's lesson, so here are some activities with their respective solutions:

1) Match the following roots with their solution:

• √366
• √814
• √99
• √163

2) Mention between which natural numbers are the following roots: √38, √54, √22, √12, √7.

3) If the class of a school is square and the teacher tells us that it has an area of ​​625 square meters, how long is the side of that class or classroom?

So that you can verify if you have carried out the previous activities correctly, it is important that we provide you with their solutions. Thus, the solutions to the above activities are:

Activity 1: √36 = 6, √81 = 9, √9 = 3, √16 = 4

Activity 2:

• 6 < √38 < 7
• 7 < √54 < 8
• 4 < √22 < 5
• 3 < √12 < 4
• 2 < √7 < 3

Activity 3: To calculate how long the side of the class is, we have to take the square root of 625, Because as the room is square, to calculate the area the two sides that measure the same are multiplied. That is, side by side equals surface, and since we know that the side measures the same in a square, we can say that the surface is the side squared. Therefore, √625 = 25 meters across.

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