Which of the following is equal to \sqrt{ \sqrt[3]{2} }

Question

Which of the following is equal to
`\sqrt{ \sqrt[3]{2} }`

Answer 1

The equal expression is;

`2^{(1)/(6)}`

Step-by-step explanation:

Given the expression;

`\sqrt[]{\sqrt[3]{2}}`

We can simplify the expression to find which of the given expression is similar to it.

`\sqrt[]{\sqrt[3]{2}}=(\sqrt[3]{2})^{(1)/(2)}=(2^{(1)/(3)})^{(1)/(2)}`

Applying the laws of indices;

`(2^{(1)/(3)})^{(1)/(2)}=2^{(1)/(3)*(1)/(2)}=2^{(1)/(6)}`

Therefore, the equal expression is;

`2^{(1)/(6)}`