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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:
23805
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Solution
Factorise each number into its prime factors.
23805 = 3 x 3 x 5 x 23 x 23
Grouping 23805 into pairs of equal factors:
23805 = (3 x 3) x (23 x 23) x 5
Here, the factor 5 does not occur in pairs. To be a perfect square, every prime factor has to be in pairs. Hence, the smallest number by which 23805 must be multiplied is 5.
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