Tick ( ) the correct answer: Which of the following numbers is a …

MCQ

Tick $(\checkmark)$ the correct answer: Which of the following numbers is a perfect cube?

A
$1152$
✓
$1331$
C
$2016$
D
$739$

✓

Answer

Correct option: B.

$1331$

$A.$ $1152$
$= 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3$
$= 2^3 \times 2^3 \times 3^2$
$\begin{array}{c|c}2&1152\\\hline2&576\\\hline2&288\\\hline2&144\\\hline2&72\\\hline2&36\\\hline2&18\\\hline3&9\\\hline3&3\\\hline&1\end{array}$
$B.$ $1131$
$= 11 \times 11 \times 11$
$= (11)^3$
$\begin{array}{c|c}11&1331\\\hline11&121\\\hline11&11\\\hline&1\end{array}$
$C.$ $2016$
$= 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 7$
$= 2^3 \times 2 \times 2 \times 3 \times 3 \times 7$
$\begin{array}{c|c}2&2016\\\hline2&1008\\\hline2&504\\\hline2&252\\\hline2&126\\\hline3&63\\\hline3&21\\\hline7&7\\\hline&1\end{array}$
$D.$ $739$
$= 1 \times 739$
We see that $1331$ is a perfect cube.

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