By what least number should 2450 be multiplie | vedclass

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Question

(D) To find the least number by which $2450$ should be multiplied to make it a perfect square,we first find its prime factorization.$2450 = 2 	imes 1

Vedclass · Accepted Answer

$2$

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(D) To find the least number by which $2450$ should be multiplied to make it a perfect square,we first find its prime factorization.$2450 = 2 	imes 1225$$2450 = 2 	imes 5 	imes 245$$2450 = 2 	imes 5 	imes 5 	imes 49$$2450 = 2 	imes 5^2 	imes 7^2$In the prime factorization,the prime factors $5$ and $7$ appear in pairs ($5^2$ and $7^2$),but the prime factor $2$ does not have a pair.To make $2450$ a perfect square,we must multiply it by $2$ so that all prime factors appear in pairs.Therefore,the required least number is $2$.

By what least number should $2450$ be multiplied so that the resulting number is a perfect square?

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