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})^{(1)/(2)}`
`[\because √(x)=x^{(1)/(2)}]`

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

`=6^{(1)/(3)*(1)/(2)}`
`[\because (a^m)^n=a^(mn)]`

`=6^{(1)/(6)}`

Therefore, the correct option is A.