Question

Find the cube root of the following natural number 1157625 .

Answer 1

Cube root by factors:
On factorising 1157625 into prime factors, we get:

\[1157625 = 3 \times 3 \times 3 \times 5 \times 5 \times 5 \times 7 \times 7 \times 7\]

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

\[\sqrt[3]{1157625} = 3 \times 5 \times 7 = 105\]