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Question
Find the smallest number by which the given number must bew multiplied so that the product is a perfect square:
12150
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Solution
12150 = 2 x 3 x 3 x 3 x 3 x 3 x 5 x 5
Grouping 12150 into pairs of equal factors:
12150 = (3 x 3 x 3 x 3) x (5 x 5) x 2 x 3
Here, 2 and 3 do not occur in pairs. To be a perfect square, every prime factor has to be in pairs. Hence. the smallest number by which 12150 must be multiplied is 2 x 3, i.e. by 6.
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