Question

What is the smallest number by which 648 must be multiplied so that the product becomes a perfect square?

• A. 2
• B. 3
• C. 5
• D. 7

Answer 1

The correct option is A 2

Prime factorisation of a perfect square has an even number of each prime factor.

$648=2\times 2\times 2\times 3\times 3\times 3\times 3$
In the prime factorisation of 648, the number of 2's are 3 and the number of 3's are 4.
So, 648 can be multiplied by 2 to make it a perfect square.