Chapter 9.1, Problem 3E

To determine

To Find: if the expression $\frac{1}{3}\sqrt{2x}$ and $\sqrt{\frac{2x}{9}}$ are equivalent.

Answer to Problem 3E

Yes, the expression $\frac{1}{3}\sqrt{2x}$ and $\sqrt{\frac{2x}{9}}$ are equivalent

Explanation of Solution

Given information:

  $\frac{1}{3}\sqrt{2x}$ and $\sqrt{\frac{2x}{9}}$

Calculation:

  $\sqrt{\frac{2x}{9}}$

Simplify

  $\begin{array}{l}=\frac{\sqrt{2x}}{\sqrt{9}}\\ =\frac{\sqrt{2x}}{3}\\ =\frac{1}{3}\sqrt{2x}\end{array}$

Thus $\frac{1}{3}\sqrt{2x}$ and $\sqrt{\frac{2x}{9}}$ are equivalent.