Question

Find the cube root of each of the following natural numbers:
$1728$

Answer 1

Step: Find the cube root of $1728$

Resolving $1728$ into prime factors

$\begin{array}{cc}2& 1728\\ 2& 864\\ 2& 432\\ 2& 216\\ 2& 108\\ 2& 54\\ 3& 27\\ 3& 9\\ 3& 3\\ & 1\end{array}$

$1728=2\times 2\times 2\times 2\times 2\times 2\times 3\times 3\times 3$
Now, by grouping the factors into
the triplets of equal factors, we get,

$1728=(2\times 2\times 2)\times (2\times 2\times 2)\times (3\times 3\times 3)$

$\therefore \sqrt[3]{31728}=2\times 2\times 3$
$=12$

Hence, the cube root of $1728$ is $12$.