Find the smallest number when it is multiplied by 392 , then the product is perfect cube.
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Find the smallest number when it is multiplied by 392 , then the product is perfect cube.

(a) 3

(b) 5

(c) 6

(d) 7
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Solution:

$$

\begin{aligned}

\begin{array}{r|l}

2 & 392 \\

\hline 2 & 196 \\

\hline 2 & 98 \\

\hline 7 & 49 \\

\hline & 7 \\

\therefore \quad 392= & 2 \times 2 \times 2 \times 7 \times 7 \\

= & (2)^{3} \times 7 \times 7

\end{array}

\end{aligned}

$$

$\therefore$ The required no. $=7$; Ans.

Therefore, the correct option is (D)

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