# Find the Cube Root of the Following Rational Number 0.003375 . - Mathematics

Sum

Find the cube root of the following rational number 0.003375 .

#### Solution

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

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

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

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#### APPEARS IN

RD Sharma Class 8 Maths
Chapter 4 Cubes and Cube Roots
Exercise 4.4 | Q 6.2 | Page 30