# Evaluate: 3 √ 36 × 3 √ 384 - Mathematics

Sum

Evaluate:

$\sqrt[3]{36} \times \sqrt[3]{384}$

#### Solution

36 and 384 are not perfect cubes; therefore, we use the following property:

$\sqrt[3]{ab} = \sqrt[3]{a} \times \sqrt[3]{b}$   for any two integers a and b

$\therefore \sqrt[3]{36} \times \sqrt[3]{384}$

$= \sqrt[3]{36 \times 384}$

$= \sqrt[3]{\left( 2 \times 2 \times 3 \times 3 \right) \times \left( 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \right)}$        (By prime factorisation)

$= \sqrt[3]{\left\{ 2 \times 2 \times 2 \right\} \times \left\{ 2 \times 2 \times 2 \right\} \times \left\{ 2 \times 2 \times 2 \right\} \times \left\{ 3 \times 3 \times 3 \right\}}$

$= 2 \times 2 \times 2 \times 3$

$= 24$

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Class 8 Maths
Chapter 4 Cubes and Cube Roots
Exercise 4.4 | Q 13.1 | Page 31