Question

Find the cube root of the following rational number 0.003375 .

Answer 1

We have: 

\[0 . 003375 = \frac{3375}{1000000}\]

∴ \[\sqrt[3]{0 . 003375} = \sqrt[3]{\frac{3375}{1000000}} = \frac{\sqrt[3]{3375}}{\sqrt[3]{1000000}}\]

Now
On factorising 3375 into prime factors, we get:

\[3375 = 3 \times 3 \times 3 \times 5 \times 5 \times 5\]

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

\[3375 = \left\{ 3 \times 3 \times 3 \right\} \times \left\{ 5 \times 5 \times 5 \right\}\]

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

\[\sqrt[3]{3375} = 3 \times 5 = 15\]

Also

\[\sqrt[3]{1000000} = \sqrt[3]{100 \times 100 \times 100} = 100\]

∴ \[\sqrt[3]{0 . 003375} = \frac{\sqrt[3]{3375}}{\sqrt[3]{1000000}} = \frac{15}{100} = 0 . 15\]