We can start by factoring 216:
216 = 2^3 × 3^3
To make C a perfect square, we need to have each prime factor appear an even number of times. Since 2 appears 3 times, we need to add one more factor of 2. This means we want k to be 2^1 = 2.
Checking, we have:
C = 216k = 216(2) = 2^3 × 3^3 × 2 = (2^2 × 3^2)^2 = 36^2
Therefore, the least value of k that will make C a perfect square is k = 2.
C=216k, find the least value of k that will make C a perfect square
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