Mark ( ) against the correct answer: By what least number should … - Vidyadip

MCQ

Mark $(\checkmark)$ against the correct answer: By what least number should $324$ be multiplied to get a perfect cube?

A
$12$
B
$14$
C
$16$
✓
$18$

✓

Answer

Correct option: D.

$18$

$\begin{array}{c|c}2&324\\\hline2&162\\\hline3&81\\\hline3&27\\\hline3&9\\\hline3&3\\\hline&1\end{array}$
$324=2\times2\times3\times3\times3\times3$
$=2\times2\times3\times(3)^3$
Therefore, to show that the given number is the product of three triplets,
we need to multiply $324$ by $(2 \times 3 \times 3).$
In other words, we need to multiply $324$ by $18$ to make it a perfect cube

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