Question

$2\sqrt[3]{34}$ express in pure surd form as

• A. $\sqrt[1]{116}$
• B. $\sqrt[3]{318}$
• C. $\sqrt[3]{332}$
• D. $\sqrt[4]{442}$

Answer 1

Answer: (C)

$\sqrt[3]{332}$

Given,

$2\sqrt[3]{34}$

On solving the above surd, we get

$2\sqrt[3]{34}=2\sqrt[3]{32^2}$

$2\sqrt[3]{34}=2\left(2^{\frac{2}{3}}\right)$ ......$[\because \sqrt[a]{ab}=b^{\frac{1}{a}}]$

$2\sqrt[3]{34}=2^{(1+\frac{2}{3})}$ ......$[\because a^m\times a^n=a^{m+n}]$

$2\sqrt[3]{34}=2^{\frac{5}{3}}$

$2\sqrt[3]{34}=\sqrt[3]{32^5}$

$2\sqrt[3]{34}=\sqrt[3]{332}$

Hence, option $\left(c\right)$ is correct answer.