Question

Find the cube root of the following natural number 33698267 .

Answer 1

Cube root by factors:
On factorising 33698267 into prime factors, we get:

\[33698267 = 17 \times 17 \times 17 \times 19 \times 19 \times 19\]

On grouping the factors in triples of equal factors, we get:

\[33698267 = \left\{ 17 \times 17 \times 17 \right\} \times \left\{ 19 \times 19 \times 19 \right\}\]

Now, taking one factor from each triple, we get:

 

\[\sqrt[3]{33698267} = 17 \times 19 = 323\]