Question

6 1/6 6 1/3 6 2/3 6 3/2

Answer 1

Given:

The expression is

$\sqrt{\sqrt[3]{6}}$

To find:

The simplified form of the given expression.

Solution:

We have,

$\sqrt{\sqrt[3]{6}}$

Using the properties of radical and exponent, we get

$=(\sqrt[3]{6})^{\frac{1}{2}}$                     $[\because \sqrt{x}=x^{\frac{1}{2}}]$

$=\left(6^{\frac{1}{3}}\right)^{\frac{1}{2}}$                  $[\because \sqrt[n]{x}=x^{\frac{1}{n}}]$

$=6^{\frac{1}{3}\times\frac{1}{2}}$                    $[\because (a^m)^n=a^{mn}]$

$=6^{\frac{1}{6}}$

Therefore, the correct option is A.