Question

The value of 22−−√3−−−−√4 is equal to
(a) 2–16
(b) 2-6
(c) 216
(d) 26​

Answer 1

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Answer 2

Note: the given question is incorrect as it should be as follows:

The value of $\[\sqrt[4]{{\sqrt[3]{{{2^2}}}}}\]$ is equal to

(a) $2^{\frac{1}{6} }$                     (b) $2^{6}$                      (c) 216                  (d) 26​

Given:  $\[\sqrt[4]{{\sqrt[3]{{{2^2}}}}}\]$.

To find: the value of the given expression.

Solution:

Simplify the given expression.

$\[\sqrt[4]{{\sqrt[3]{{{2^2}}}}} = {\left( {{{\left( {{2^2}} \right)}^{\frac{1}{3}}}} \right)^{\frac{1}{4}}}\]$

$\[ \Rightarrow \sqrt[4]{{\sqrt[3]{{{2^2}}}}} = {2^{2 \times \frac{1}{3} \times \frac{1}{4}}}\]$

$\[ \Rightarrow \sqrt[4]{{\sqrt[3]{{{2^2}}}}} = {2^{\frac{1}{6}}}\]$

Therefore, the value of $\[\sqrt[4]{{\sqrt[3]{{{2^2}}}}}\]$ is $\[{2^{\frac{1}{6}}}\]$.

Hence, the correct answer is option (a). i.e., $\[{2^{\frac{1}{6}}}\]$.