Evaluate:
(i) \( \sqrt[3]{36} \times \sqrt[3]{384} \)
(ii) \( \sqrt[3]{96} \times \sqrt[3]{144} \)
(iii) \( \sqrt[3]{100} \times \sqrt[3]{270} \)
(iv) \( \sqrt[3]{121} \times \sqrt[3]{297} \)

To find: 

We have to evaluate the given expessions.

Solution:

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

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

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

$=\sqrt[3]{3^{3} \times 2^{3} \times 2^{3} \times 2^{3}}$

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

$=24$

(ii) $\sqrt[3]{96} \times \sqrt[3]{144}=\sqrt[3]{96 \times 144}$

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

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

$=\sqrt[3]{2^{3} \times 2^{3} \times 2^{3} \times 3^{3}}$

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

$=24$

(iii) $\sqrt[3]{100} \times \sqrt[3]{270}=\sqrt[3]{100 \times 270}$

$=\sqrt[3]{27000}$

$=\sqrt[3]{1000 \times 27}$

$=\sqrt[3]{10 \times 10 \times 10 \times 3 \times 3 \times 3}$

$=\sqrt[3]{10^{3} \times 3^{3}}$

$=10 \times 3$

$=30$

(iv) $\sqrt[3]{121} \times \sqrt[3]{297}=\sqrt[3]{121 \times 297}$

$=\sqrt[3]{11 \times 11 \times 11 \times 3 \times 3 \times 3}$

$=\sqrt[3]{(11)^{3} \times(3)^{3}}$

$=11 \times 3$

$=33$

Tutorialspoint

Updated on: 10-Oct-2022

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