Question:
Is 176 a perfect square? If not, find the smallest number by which it should be multiplied to get a perfect square.
Solution:
First we have to find out the factors by using prime factorisation method.
So, prime factors of 176 = 2 × 2 × 2 × 2 × 11
Now, grouping the prime factors = (2 × 2) × (2 × 2) × (11)
= 22 × 22 × 11
Factor 11 has no pair.
∴176 is not a perfect square.
The smallest number it should be multiplied to get a perfect square is 11.
Then,
176 × 11 = 1936
Factors of 1936 = 2 × 2 × 2 × 2 × 11 × 11
= √1936
= √(22 × 22 × 112)
= 2 × 2 × 11
= 44
∴Square root of 1936 is 44.