Square Root Formula


The square root formula helps in representing any number in the form of its square root. The square root of any number is that value, which when multiplied with itself gives the original number. It is represented using "√" symbol. Every number has two square roots, one with positive value, and the other negative. Let us understand the square root formula using solved examples in the following section.

What is the Square Root Formula?

The square root of any number is given as the number raised to the power 1/2. While calculating the square root of any number, we take both the negative and positive values as the square root after calculation. The square root formula for a perfect square would give an integer as the result. Square root of a negative number can never be a real number. The square root formula of a number, x is given as,  

√x = x1/2

Suppose, x is any number such that, x = y × y, the formula to calculate square root of x will be,

√x = √(y × y) = y

where, y is square root of any number x. This also means that if the value of y is an integer, then x would be a perfect square.

Let us have a look at a few solved examples to understand square root formula better. 

Solved Examples Using Square Root Formula

Example 1: Using the square root formula, calculate the square root of 144.

Solution:     

To find: square root of 144

From prime factorization of 144, we get,

144 = 2 × 2 × 2 × 2 × 3 × 3 

= (2 × 2 × 3)2

Using square root formula,

√144 = ± [(2 × 2 × 3)1/2]2

√144 = ±12

Answer:  Square root of 144 = ±12

Example 2: Using the square root formula, calculate the square root of 225. 

Solution:       

To find: square root of 225

From prime factorization of 225, we get,

225 = 3 × 3 × 5 × 5  

= (3 × 5)2

Using the square root formula,

√225 = ±[(3 × 5)1/2]2

√225 = ±15

Answer: Square root of 225 = ±15