Square Root

Learn The Definition And How To Find The Square Roots Of Numbers With Formulas And Examples

As kids progress through the grades, they start learning more and more complex math concepts. Square root and squares are one such topic that kids start learning in grades 4 and 5. But, what are they? the square root of a number is another number, which you get when the original number is multiplied by itself. Before introducing this concept to the little ones, ensure they know the multiplication table for kids. The square root can be expressed as a x where a is the natural number and the x is the square root of the number.

What is Square Root?

In math, square roots are the factor of a number, which gives the original number when it’s multiplied by itself. It is represented by the symbol √. Consider this formula, if p is the square root of q, it implies that p x p = q. 

Here is an example to help you understand better, 4 is the square root of 16. To get 16, 4 is multiplied by itself. In this context, the exponent is 2, it is known as a square.

According to mathematical concepts, square roots and squares are reverse operations. The square of any numeral is the value of power 2 of the number. Another fact about squares and square roots is that they are always a positive number. Here is a list of square roots to help your child learn the concept easily given below:

List Of Square Roots

Square root of 1Square root of 11
Square root of 2Square root of 12
Square root of 3Square root of 13
Square root of 4Square root of 14
Square root of 5Square root of 15
Square root of 6Square root of 16
Square root of 7Square root of 17
Square root of 8Square root of 18
Square root of 9Square root of 19
Square root of 10Square root of 20


The square root of a digit is the value of power ½ of that number. In simple words, the square root is the number that is multiplied by itself to obtain the actual number. It is expressed as ‘ ‘.

Also, refer to Multiplication Worksheets, available at Osmo.

How to Find The Square Root?

Once your child has understood the definition, it’s time to teach how to find the square root of a number. Some kids might find it difficult to grasp the concept easily. Therefore, you can start with simpler numbers that are perfect squares, which is a number that can be expressed as the product of two equal integers. Finding the square roots of perfect square is quite easy and kids will learn it faster. 

Here are four different methods to determine the square roots of numbers:

  • Repeated Subtraction Method
  • Estimation Method
  • Prime Factorization Method
  • Long Division Method

Table Of Square Roots

Here is a table to help your kids learn easily. The table has a list of the square roots of numbers from 1 to 10. This list includes both perfect squares and numbers that are non-perfect squares.

NumberSquare Root

Square Root Formula

One thing that makes it easy to determine square roots of numbers is a formula. Here is a simple formula you can use: √x= x1/2

According to this formula, 41/2 = √4 = √(2×2) = 2. 

Determining Square Roots Of Negative Numbers

Now that you know how to find the square roots of positive integers, how do you find the same for a negative integer? A square is always 0 or positive, so negative numbers don’t have real square roots.

But, here is an easy formula you can use: √(-y)= i√y. Here, i is the square root of -1. 

For instance, let’s determine the √ -25. 

√(-25)= √25 × √(-1) 

Since negative numbers don’t have real square roots, let’s consider √(-1)= i

√(-25)= √25 × √(-1) = 5i 

Therefore, the √-25 is 5i.

Getting kids to learn math can be difficult. Involve kids in fun activities like math games for kids and worksheets to help them learn in a fun and engaging way. Check Osmo’s kids learning section to find more fun ways to help kids learn.

Frequently Asked Questions on Square Root

What Is A Square Root?

A square root is a number that is obtained when a number is multiplied by itself. For example, 10 is the square root of 100; that is, 10 x 10 = 100. The square root is denoted by a symbol, √.

How is the square root of a number calculated?

The square root of a number is calculated using this formula. The formula for the square root is used to determine the square root of a digit. The exponent formula to find out the square root is, n√y y n = y1/n. Here, n= 2, is called a square root. We can use any of these simple ways for determining the square root, like, long division, prime factorization, and many more.

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