If $k$ is a positive integer, what is the smallest value for $k$ to make $60 k$ a perfect square?

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Solution

The correct option is B 15
Prime factor of $60 =$ $2 \times 2 \times 3 \times 5$
To make a perfect square we need to multiply it by $=$ $3 \times 5$
Because to make a perfect square, prime factor may be in the group of two.
$∴$ the value of $k =$ $5 \times 3 = 15$

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