Question

The rationalising factor of $2\sqrt[3]{35}$ is _________.

• A. $\sqrt[3]{35}$
• B. $\sqrt[3]{35^2}$
• C. $5^2$
• D. $5^3$

Answer 1

Answer: (B)

$\sqrt[3]{35^2}$

Rationalising factor is a term with which a term is multiplied or divided to make the whole term rational.

Here, $2\sqrt[3]{35}$ can be written as $2\times 5^{1/3}$.

In order to make it rational, we need to eliminate the surd.

Hence multiply it with a term so as to rationalise $\sqrt[3]{35}$.

Multiplying by $\sqrt[3]{35^2}$ we get, $2\times 5^{1/3}\times 5^{2/3}=2\times 5^{3/3}=10$, hence rationalised.

Therefore, $\sqrt[3]{35^2}$ is the required rationalising factor.

Hence, option $B$ is correct.