Question

Use prime factorization method to find the cube root of $10648$

Answer 1

Step $1:$ Finding the prime factorization of $10648$:

The given number is $10648$

On the prime factorisation of $10648$, we get the prime factors as

$10648=2\times 2\times 2\times 11\times 11\times 11$

Step $2:$ Finding the cube root of $10648$:

By grouping the equal prime factors of $10648$ in triplets, we get,

$\begin{array}{rcl}\sqrt[3]{10648}& =& \sqrt[3]{2\times 2\times 2\times 11\times 11\times 11}\\ & =& \sqrt[3]{\left(2\times 2\times 2\right)\times \left(11\times 11\times 11\right)}\\ & =& 2\times 11\\ & =& 22\end{array}$

Hence, the cube root of $10648$ is $22$.