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.

Question

Mathematics

Tristin Christian

6 January, 14:34

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.

+3

Answers (1)

Know the Answer?

Meghan Mcdaniel · Answer 1

22

Step-by-step 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

Given that the prime factorisation of 198 is 2x (3*3) x11. State the minimum integer value ofn such that square root of 198n is a natural number.

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.