Square Root & Cube Root: Prime Factorisation Method, Division Method, Formula and Tricks with Problem (Question) and Solutions


The resultant number of a product of a number with itself, is known as square of given number.

Square Root

The square root of given number is that number whose square is equal to the given number. To represent a square root of a number we use a notation with number.


Perfect Square

If square root of a number is a natural number, then that number must be a perfect square.

Methods to Find Square Root

Different methods to find the square root of given number are as follows

(i) Prime Factorisation Method

In this method, we find prime factors of given number and make pairs of like prime factors. The product of one factor from each pair is the square root of given number.

Square root of only perfect square numbers can be calculated by this method.

Ex :- √8281 =

(a) 89

(b) 97

(c) 93

(d) 91

Sol :- 8281 = 7 x 7 x 13 x 13


(ii)Division Method

In this method, we make pair from right side. Divide outermost left side pair or digit by a number whose square is less or equal to that pair or digit and write this number at the place of divisor and quotient. Find the remainder. Now write next pair to the right of remainder.

Now at the place of divisor write double of quotient and write a digit whose product with new divisor is less than or equal to new dividend. We find remainder and repeat this procedure until we get zero as remainder or all pairs are finished.

Ex. Find the square root of 30625

(a) 125


(c) 925

(d) 225



Square Root of Decimal Numbers

If in a given decimal, number, the number of digits after decimal are not even, then we put a 0 (zero) at the extreme right, So that these are even number of digits after the decimal point. Now, periods are marked as marked in previous explanation starting from right hand side before the decimal point and from the left hand after the decimal digit.

After the periods are marked then previous method is used to find the square root.

Ex:- Find the square root of 13.5424

(a) 6.68

(b) 36.8

(c) 3.30

(d) 3.28




The cube of a number is the number which is obtained by multiplying that number by itself twice.


Cube Root

The cube root of a given number is that number, which when multiplied by itself twice, produces the given number. It is denoted by

Perfect Cube

if cube root of a number is a natural number, then that number must be a perfect cube.

Method to Find Cube Root

Prime Factorisation Method

To find the cube root of given number, first find the prime
factors of given number. Make triplet of all same prime
factors. he product of one factor from each triplet is the
cube root of the given number


Important Formulae

Formula 1

Formula 2

Formula 3


Formula 4

(1)pq=pq (a) (b) (c) (d)

Formula 5

Leave a Comment