Question

By prime factorisation, check whether the following numbers are perfect squares or not. Also, find the number whose square they are.

a) 361
b) 1764
c) 666
d) 676​

Answer 1

Answer:

To find the square root of a perfect square by using the prime factorization method when a given number is a perfect square:

Step I: Resolve the given number into prime factors.

Step II: Make pairs of similar factors.

Step III: Take the product of prime factors, choosing one factor out of every pair.

Examples on square root of a perfect square by using the prime factorization method:

1. Find the square root of 484 by prime factorization method.

Solution:

Resolving 484 as the product of primes, we get



484 = 2 × 2 × 11 × 11 

√484 = √(2 × 2 × 11 × 11) 

= 2 × 11

Therefore, √484 = 22