Question

is 2352 a perfect square? if not ,find the square. smallest number by which 2352 must multiple so that the product is a perfect square find the square root of new number

Answer 1

The prime factorisation of 2352 is,2352 = 2 × 2 × 2 × 2 × 7 × 7 × 32352 = 22 × 22 × 72 × 3Since prime factor 3 does not occur in pair,hence 2352 is not a perfect squareThe smallest multiple of 2352 which is a perfect square is 2352 × 3 = 7056Now, 2352 = 22 × 22 × 72 × 32Hence,  2352−−−−√ = 22 × 22 × 72 × 32 −−−−−−−−−−−−−−−−−√ = 2 × 2 × 7 × 3 = 84

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