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Cube and Cube Roots — MATHS STD 8 — Question

Gujarat BoardEnglish MediumSTD 8MATHSCube and Cube Roots1 Mark
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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