Question

Find the smallest possible integer value of k for which 264k is a perfect square.

Answer 1

k = 66.

Explanation:

Find the prime factors of 264

264 = 2 * 2 * 2 * 3 * 11

The nearest perfect square will contain one more 2, one more 3 and one more 11

= 264 * 2 * 3 * 11

= 17424.

Answer 2

Explanation:

264k

= 2³ * 3 * 11 * k

Hence, k = 2 * 3 * 11 = 66.