helpmewithmyhw24 helpmewithmyhw24

31-12-2019
Mathematics

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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.

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31-12-2019

Answer:

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

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