Question

is 2532 a perfect square? if not ,find the smallest multiple of 2532 which is a perfect square.

Answer 1

p is a prime factor of a perfect square, then the maximum k for which pk is a factor, then k MUST be an even number. We prime factor 2352 with a factor tree: 2352 / \ 2 1176 / \ 2 588 / \ 2 294 / \ 2 147 / \ 3 49 / \ 7 7 So 2352 = 24∙3∙72 The primes 2 and 7 already have even powers, so we must multiply by 3 so that the 3 will also have an even power.
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