## What is a Square Root?

Square root is one of the most important functions in Mathematics which has a wide range of applications in day to day life and also scientific calculations. Square root of any number in Mathematics is that number which when multiplied by itself gives the product equal to the number whose square root is to be determined. Square root of a number is represented as the number written within the symbol ‘√’. Square root of a number ‘x’ is written as √x. Square root of a number can be represented in exponential form as the number to the power ½. Square root of a number ‘x’ can be written in exponential form as (x)1/2.

### What is a Perfect Square Number and Square Root Formula?

It is very important to understand what is a square root of a perfect square number before making yourself clear about what is a root in math. What is a perfect square number in Mathematics can be that number which is obtained as a product by multiplying any integer by itself. The square root formula when used for perfect square numbers will yield a number which is an integer as the answer. i.e. Square root of a perfect square number is always an integer.

### What is a Root in Math?

There are several methods to find the square root of a number among which a few familiar ones are:

Prime factorization method

Repeated Subtraction Method

Average Method

Guess and check method

Number line method

Long division method

### Finding Square Root Formula by Prime Factorization Method

Prime factorization method is a method in which the numbers are expressed as a product of their prime factors. The identical prime factors are paired and the product of one element from each pair gives the square root of the number. This method can also be used to find whether a number is a perfect square or not. However, this method cannot be used to find the square root of decimal numbers which are not perfect squares.

Example: Evaluate the root of 576.

Solution:

576 is factorized into its prime factors as follows.

So, 576 can be written as a product of prime numbers as:

576 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3

Square root of 576 = 2 x 2 x 2 x 3 = 24

### Square Root Formula Using Repeated Subtraction Method

This is a method in which the number whose square root is to be determined is repeatedly subtracted by the consecutive odd number till the difference becomes zero. The number of subtractions gives the root of the number.This method can only be used to find the square root of perfect square numbers.

Example: Estimate the Square root of 16

Solution:

The number is subtracted from odd numbers starting from 1.

16 - 1 = 15

15 - 3 = 12

12 - 5 = 7

7 - 7 = 0

Number of subtractions here is 4. So, the square root of 16 is 4.

### Average Method of Square Root Formula:

In this method, the concept of average is used to find the square root of a given decimal number. This method can be conveniently used to find the square root of whole numbers upto a few decimal places.

Example: Evaluate the square root of 3 using the average method.

Solution:

The two square numbers in between which ;3’ lies are 1 and 4. So, the square root of 3 lies between 1 and 2. Find the average of these two numbers to get the square root of 3.

Square root of 3 = (1 + 2)/ 2 = 3/ 2 = 1.5 which is not accurate. So, finding the average is further continued as

Square root of 3 = (1.5 + 2)/2 = 1.75 which is approximately equal to square root of 3.

### Fun Facts About Square Root Formula:

Square and square root operations are inverse mathematical operations with respect to each other.

Square root of a square of a number is the number itself.

The square of square root of a number is the number itself.

### Conclusion

The article has presented complete insight about the Square Root formula that will help students to practice and learn.

## FAQs on Square Root Formula

**1. What is a Perfect Square Number? What is Root in Mathematics of Perfect Square Number Properties?**

Any number whose square root is an integer is called a perfect square number.

The natural numbers ending with 2, 3, 7 and 8 do not have perfect square roots. Only the numbers ending with 0, 1, 4, 5, 6 and 9 may have square roots.

Numbers ending with an odd number of zeros do not square roots. Numbers ending with an even number of zeros have half the number of zeros in their square root.

Square root of an even square number is even and that of an odd square number is odd.

Every number has two roots: one positive root and one negative root.

Square roots of negative numbers are imaginary.

**2. What is a Root in Math? How is it Found Using Guess and Check Method?**

In mathematics, the square root of a number is that number which when multiplied by itself gives the number whose square root is to be found as the product.

**Guess and Check Method:**

In this method, the square root of a number is determined by finding the square numbers between which the number lies. Assumptions are made and the square root is determined by trial and error method.

Example: If ‘x’ = 7, find the square root of x by guess and check method.

Solution:

‘7’ lies between two square numbers 4 and 9. So, its square root lies between 2 and 3.

Let us assume that the square root of ‘7’ is 2.5.

2.5 x 2.5 = 6.25 which is very less than 7.

So let us take the square root of 7 as 2.6

2.6 x 2.6 = 6.76 which is also less than 7

Let us assume the square root of 7 as 2.7

2.7 x 2.7 = 7.29 which is more than 7.

So, from the above results, it is evident that the square root of 7 lies between 2.6 and 2.7

Let us take root 7 as 2.65

2.65 x 2.65 = 7.022 which is almost equal to 7.

So, the square root of 7 can be approximated to 2.65. The process can be continued to get more accurate results.