Find the smallest number by which 5808 should | vedclass

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Question

(B) To find the smallest number by which $5808$ should be multiplied to make it a perfect square,we first find its prime factorization.$5808 = 2 	ime

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(B) To find the smallest number by which $5808$ should be multiplied to make it a perfect square,we first find its prime factorization.$5808 = 2 	imes 2904 = 2 	imes 2 	imes 1452 = 2 	imes 2 	imes 2 	imes 726 = 2 	imes 2 	imes 2 	imes 2 	imes 363 = 2 	imes 2 	imes 2 	imes 2 	imes 3 	imes 121 = 2^4 	imes 3 	imes 11^2$.In a perfect square,every prime factor must have an even exponent.Here,the prime factor $3$ has an exponent of $1$,which is odd.To make the exponent of $3$ even (i.e.,$2$),we must multiply the number by $3$.Therefore,the smallest number to be multiplied is $3$.

Find the smallest number by which $5808$ should be multiplied so that the product becomes a perfect square.

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