Chapter A.1, Problem 51E

Solution

Write using a single radical.

  $\sqrt[4]{2x}$ .

Given:

The given expression is $\sqrt{\sqrt{2x}}$ .

Concept Used:

• Radical - The v symbol that is used to denote square root or nth roots.

Calculation:

The given expression is $\sqrt{\sqrt{2x}}$ .

  $\begin{array}{c}\sqrt{\sqrt{2x}}=\sqrt{{(2x)}^{1/2}}\\ ={\left({(2x)}^{1/2}\right)}^{1/2}\\ ={\left(2x\right)}^{\frac{1}{2}\cdot \frac{1}{2}}\\ ={\left(2x\right)}^{1/4}\\ =\sqrt[4]{2x}\end{array}$

Thus the single radical expression of $\sqrt{\sqrt{2x}}$ is $\sqrt[4]{2x}$ .