Question

Evaluate: 

\[\sqrt[3]{121} \times \sqrt[3]{297}\]

 

Answer 1

121 and 297 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

\[\therefore \sqrt[3]{121} \times \sqrt[3]{297}\]

\[ = \sqrt[3]{121 \times 297}\]

\[= \sqrt[3]{\left( 11 \times 11 \right) \times \left( 3 \times 3 \times 3 \times 11 \right)}\]                (By prime factorisation)

\[= \sqrt[3]{\left\{ 11 \times 11 \times 11 \right\} \times \left\{ 3 \times 3 \times 3 \right\}}\]

\[ = 11 \times 3\]

\[ = 33\]

Thus, the answer is 33.