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 $=252 \times 7=1764$
$\therefore \sqrt{1764}=2 \times 3 \times 7=42$