# Find the Cube Root of the Following Natural Number 74088000 . - Mathematics

Sum

Find the cube root of the following natural number 74088000 .

#### Solution

Cube root by factors:
On factorising 74088000 into prime factors, we get:

$74088000 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 3 \times 5 \times 5 \times 5 \times 7 \times 7 \times 7\ On grouping the factors in triples of equal factors, we get: \[74088000 = \left\{ 2 \times 2 \times 2 \right\} \times \left\{ 2 \times 2 \times 2 \right\} \times \left\{ 3 \times 3 \times 3 \right\} \times \left\{ 5 \times 5 \times 5 \right\} \times \left\{ 7 \times 7 \times 7 \right\}$
Now, taking one factor from each triple, we get:
$\sqrt[3]{74088000} = 2 \times 2 \times 3 \times 5 \times 7 = 420$

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Class 8 Maths
Chapter 4 Cubes and Cube Roots
Exercise 4.3 | Q 4.09 | Page 22