Find the smallest number by which 216 should | vedclass

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Question

(C) To find the smallest number by which $216$ should be divided to make it a perfect square,we first find the prime factorization of $216$.$216 = 2 \

Vedclass · Accepted Answer

$6$

Vedclass · Answer

(C) To find the smallest number by which $216$ should be divided to make it a perfect square,we first find the prime factorization of $216$.$216 = 2 	imes 2 	imes 2 	imes 3 	imes 3 	imes 3 = (2 	imes 2) 	imes (3 	imes 3) 	imes 2 	imes 3 = 2^2 	imes 3^2 	imes 6$.In the prime factorization,the factors $2$ and $3$ are in pairs,but the factor $6$ (which is $2 	imes 3$) is left unpaired.To make the number a perfect square,we must divide $216$ by this remaining factor,which is $6$.Thus,$\frac{216}{6} = 2^2 	imes 3^2 = 4 	imes 9 = 36$,which is a perfect square $(6^2 = 36)$.Therefore,the smallest number is $6$.

Find the smallest number by which $216$ should be divided to make the result a perfect square.

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