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mr Goodwill [35]
3 years ago
11

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

Mathematics
1 answer:
suter [353]3 years ago
6 0

9514 1404 393

Answer:

  k = 15

Step-by-step 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

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