Given:
The expression is
[tex]\sqrt{\sqrt[3]{6}}[/tex]
To find:
The simplified form of the given expression.
Solution:
We have,
[tex]\sqrt{\sqrt[3]{6}}[/tex]
Using the properties of radical and exponent, we get
[tex]=(\sqrt[3]{6})^{\frac{1}{2}}[/tex] [tex][\because \sqrt{x}=x^{\frac{1}{2}}][/tex]
[tex]=\left(6^{\frac{1}{3}}\right)^{\frac{1}{2}}[/tex] [tex][\because \sqrt[n]{x}=x^{\frac{1}{n}}][/tex]
[tex]=6^{\frac{1}{3}\times\frac{1}{2}}[/tex] [tex][\because (a^m)^n=a^{mn}][/tex]
[tex]=6^{\frac{1}{6}}[/tex]
Therefore, the correct option is A.
