Question:
Find the smallest number by which 2925 must be divided to obtain a perfect square. Also, find the square root of the perfect square so obtained.
Solution:
Resolving into prime factors:
$2925=3 \times 3 \times 5 \times 5 \times 13$
13 is the smallest number by which the given number must be divided to make it a perfect square.
New number $=2925 \div 13=225$
$\sqrt{225}=3 \times 5=15$
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