The least number by which 10584 must be multi | vedclass

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Question

(C) To find the least number by which $10584$ must be multiplied to make it a perfect square,we first find its prime factorization.$10584 = 2 	imes 5

Vedclass · Accepted Answer

$6$

Vedclass · Answer

(C) To find the least number by which $10584$ must be multiplied to make it a perfect square,we first find its prime factorization.$10584 = 2 	imes 5292 = 2^2 	imes 2646 = 2^3 	imes 1323 = 2^3 	imes 3 	imes 441 = 2^3 	imes 3 	imes 3 	imes 147 = 2^3 	imes 3^2 	imes 3 	imes 49 = 2^3 	imes 3^3 	imes 7^2$.Grouping the prime factors into pairs: $10584 = (2^2 	imes 3^2 	imes 7^2) 	imes (2 	imes 3)$.For a number to be a perfect square,all prime factors must have even exponents.Here,the factors $2$ and $3$ have odd exponents ($1$ each).Therefore,we must multiply by $2 	imes 3 = 6$ to make all exponents even.

The least number by which $10584$ must be multiplied to make it a perfect square is

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