The value of (√(8))1/3 is · ABC26GN1906
Subject: General Aptitude · Chapter: Surds and Indices
The value of $(\sqrt{8})^{\frac{1}{3}}$ is
(a)2
(b)4
(c)$\sqrt{2}$
(d)8
Answer
Explanation
$$\begin{aligned} (\sqrt{8})^{\frac{1}{3}} & =\left(8^{\frac{1}{2}}\right)^{\frac{1}{3}}=8^{\left(\frac{1}{2} \times \frac{1}{3}\right)} \\ & =8^{\frac{1}{6}}=\left(2^{3}\right)^{\frac{1}{6}}=2^{\left(3 \times \frac{1}{6}\right)}=2^{\frac{1}{2}}=\sqrt{2} . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.
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