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How to find the smallest integer k such that 60k is a perfect square

User KevinKirkpatrick
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1 Answer

16 votes
16 votes

9514 1404 393

Answer:

k = 15

Explanation:

Look for the missing factors that make all of the factors of 60k be squares.

60 = 2² × 3 × 5

The factors 3 and 5 each have an odd exponent (1), so those two factors must be part of k.

60k = 2² × 3 × 5 × k

is a perfect square when ...

3 × 5 = k = 15

For k = 15, 60k = 900 = 30²

User Mousey
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