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3 years ago

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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