Question

Find the cube root of the following natural number 48228544 .

Answer 1

Cube root by factors:
On factorising 48228544 into prime factors, we get:

\[48228544 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 7 \times 7 \times 7 \times 13 \times 13 \times 13\]

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

\[48228544 = \left\{ 2 \times 2 \times 2 \right\} \times \left\{ 2 \times 2 \times 2 \right\} \times \left\{ 7 \times 7 \times 7 \right\} \times \left\{ 13 \times 13 \times 13 \right\}\]

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

 \[\sqrt[3]{48228544} = 2 \times 2 \times 7 \times 13 = 364\]