Question

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

Answer 1

Answer:

The equal expression is;

$2^{\frac{1}{6}}$

Explanation:

Given the expression;

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

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

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

Applying the laws of indices;

$(2^{\frac{1}{3}})^{\frac{1}{2}}=2^{\frac{1}{3}\times\frac{1}{2}}=2^{\frac{1}{6}}$

Therefore, the equal expression is;

$2^{\frac{1}{6}}$