Question

Find the cube root of each of the following natural numbers:
$1157625$

Answer 1

Step: Find the cube root of $1157625$

Resolving $1157625$ into prime factors

$\begin{array}{cc}3& 1157625\\ 3& 385875\\ 3& 128625\\ 5& 42875\\ 5& 8575\\ 5& 1715\\ 7& 343\\ 7& 49\\ 7& 7\\ & 1\end{array}$

$1157625=3\times 3\times 3\times 5\times 5\times 5\times 7\times 7\times 7$

Now, by grouping the factors into
the triplets of equal factors, we get,

$1157625=(3\times 3\times 3)\times (5\times 5\times 5)\times (7\times 7\times 7)$

$\therefore \sqrt[3]{31157625}=3\times 5\times 7$
$=105$

Hence, the cube root of $1157625$ is $105$.