Chapter 9.1, Problem 50E

To determine

To simplify: The expression $\frac{1}{\sqrt{2x}}$

Answer to Problem 50E

The required answer is $\frac{\sqrt{2x}}{2x}$

Explanation of Solution

Given information:

The given expression $\frac{1}{\sqrt{2x}}$

Calculation:

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

(Multiply by $\frac{\sqrt{2x}}{\sqrt{2x}}$ )

  $=\frac{\sqrt{2x}}{\sqrt{4x^2}}$

(Product property of square root)

  $=\frac{\sqrt{2x}}{\sqrt{4}\cdot \sqrt{x^2}}$

(Product property of square root)

  $=\frac{\sqrt{2x}}{2x}$

(Simplify)