Question

Find the cube root of 4096 .

• A. 44
• B. 16
• C. 24
• D. 34

Answer 1

The correct option is B

16

Factorise 4096 into its prime factors.
$\begin{array}{cc}2& 4096\\ 2& 2048\\ 2& 1024\\ 2& 512\\ 2& 256\\ 2& 128\\ 2& 64\\ 2& 32\\ 2& 16\\ 2& 8\\ 2& 4\\ 2& 2\\ & 1\end{array}$
Prime factors of 4096 = 2 $\times$ 2 $\times$ 2 $\times$ 2 $\times$ 2 $\times$2 $\times$ 2$\times$ 2 $\times$ 2 $\times$ 2$\times$ 2 $\times$ 2
So, cube root of 4096 = $\sqrt[3]{32^3\times 2^3\times 2^3\times 2^3}$
= 2 x 2 x 2 x 2
= 16