Find the smallest number by which 252 must be multiplied to get a perfect square.

Question:

Find the smallest number by which 252 must be multiplied to get a perfect square. Also, find the square root of the perfect square so obtained.

Solution:

Resolving into prime factors:

$252=2 \times 2 \times 3 \times 3 \times 7$

Thus, the given number must be multiplied by 7 to get a perfect square.

New number $=252 \times 7=1764$

$\therefore \sqrt{1764}=2 \times 3 \times 7=42$

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