Question

Given that the prime factorisation of 198 is 2x(3×3)x11. State the minimum integer value of

n such that square root of 198n is a natural number.​

Answer 1

22

Explanation:

198 = 2×3²×11

For 198n to be a perfect square, each prime factor must have an even exponent. So the smallest 198n would be:

198n = 2²×3²×11²

198n = 4356

n = 22