Question

Evaluate: \[\sqrt[3]{700 \times 2 \times 49 \times 5}\]

Answer 1

Property:
For any two integers a and b

\[\sqrt[3]{ab} = \sqrt[3]{a} \times \sqrt[3]{b}\]

From the above property, we have:​

\[\sqrt[3]{700 \times 2 \times 49 \times 5}\]

\[= \sqrt[3]{2 \times 2 \times 5 \times 5 \times 7 \times 2 \times 7 \times 7 \times 5}\]

∴ \[700 = 2 \times 2 \times 5 \times 5 \times 7 and 49 = 7 \times 7\]

\[= \sqrt[3]{2^3 \times 5^3 \times 7^3}\]

\[ = \sqrt[3]{2^3} \times \sqrt[3]{5^3} \times \sqrt[3]{7^3}\]

\[ = 2 \times 5 \times 7\]

\[ = 70\]