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Question
Find the square root the following by prime factorization.
27225
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Solution
Resolving 27225 into prime factors:
27225 = 3 x 3 x 5 x 5 x 11 x 11
Grouping the factors into pairs of equal factors:
27225 = (3 x 3) x (5 x 5) x (11 x 11)
Taking one factor for each pair, we get the square root of 27225:
3 x 5 x 11 = 165
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