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Evaluate: 3 √ 36 × 3 √ 384 - Mathematics

Sum

Evaluate:

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

 

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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)

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

\[ = 2 \times 2 \times 2 \times 3\]

\[ = 24\]

Thus, the answer is 24.

 

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APPEARS IN

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