Square root of a Number

A number multiplied by itself is called square of that number.

Example

Squares of a few numbers are as above.

Like the inverse operation of ‘+’ is ‘-‘,

the inverse operation of square is square root.

The square of 2 is 4. The square root of 4 is 2.

The square root of a number is always positive.

Now we will find square root of a few numbers using prime factorisation.

Example 1: Find the square root of 36

First, we will find the prime factors of 36.

Prime factorisation of 36 is as above.

Prime factors 2 and 3 occur in pairs.

Such numbers for which the prime factors occur in pairs are said to be perfect squares.

After grouping the prime factors we get the square root of 36 as 6.

Example 2: Find the square root of 625.

The prime factorisation of 625 is as above.

Observe that the factors of 625 are in pairs.

Grouping the factors, we get the square root of 625 as 25

Example 3: Find if 180 is a perfect square.

The prime factors of 180 are as above.

The prime factor 5 has no pair for it.

So 180 is not a perfect square.

To make 180 to a perfect square we have to multiply 5 on both the sides.

Now, 900 is a perfect square whose square root is 30.

Revision

The inverse operation of square is square root.

Square root of a number is aways positive.

For a perfect square, prime factors of a number occur in pairs.

Prime factorisation can be used to find the square root of a number.

The End