Question

Using prime factorisation, find the cube roots of $2197$

Answer 1

Let us first determine the factors by the method of prime factorization of $2197$

So, prime factors of $2197=13\times 13\times 13$

On grouping and pairing the obtained factors we get$=(13\times 13\times 13)$

Then, cube root of $2197$$=\sqrt[3]{2197}$

$=\sqrt[3]{13\times 13\times 13}$

$=\sqrt[3]{{\left(13\right)}^3}$

$=13$

∴The cube root of $2197is13$