Q. 8.100 - Intermediate Algebra

Question

In the following exercise ,simplify

  $$\begin{gathered} \left(a\right) \frac{6}{\sqrt{5}} \\ \left(b\right) \sqrt{\frac{7}{18}} \\ \left(c\right) \frac{5}{\sqrt{5x}} \end{gathered}$$

Step-by-Step Solution

Answer

$$\begin{gathered} \left(a\right) \frac{6\sqrt{5}}{5} \\ \left(b\right) \frac{\sqrt{14}}{6} \\ \left(c\right) \frac{\sqrt{5x}}{x} \end{gathered}$$

Part (a) Step 1. Given information.

The expression given :

$\frac{6}{\sqrt{5}}$

Part (a) Step 2. Finding the solution.

Multiply numerator and denominator by the same factor.

Multiply numerator and denominator $\sqrt{5}$.

$$\begin{gathered} \frac{6}{\sqrt{5}}=\frac{6}{\sqrt{5}}\times \frac{\sqrt{5}}{\sqrt{5}} \\ =\frac{6\sqrt{5}}{5} \end{gathered}$$

Part (b) Step 1. Given information.

Given expression:

$\sqrt{\frac{7}{18}}$

Part (b) Step 2. Finding solution.

Multiply numerator and denominator by the same factor.

Multiply numerator and denominator $\sqrt{18}$.

$$\begin{gathered} \sqrt{\frac{7}{18}}=\frac{\sqrt{7}}{\sqrt{18}}\times \frac{\sqrt{18}}{\sqrt{18}} \\ =\frac{\sqrt{7}\sqrt{18}}{18} \\ =\frac{\sqrt{7}.9}{18} \\ =\frac{\sqrt{7}}{2} \end{gathered}$$

Part (c) Step 1. Given information

Given expression:

$\frac{5}{\sqrt{5x}}$

Part (c) Step 2. Finding the solution.

Multiply numerator and denominator by the same factor.

Multiply numerator and denominator $\sqrt{5x}$.

$$\begin{gathered} \frac{5}{\sqrt{5x}}=\frac{5}{\sqrt{5x}}\times \frac{\sqrt{5x}}{\sqrt{5x}} \\ =\frac{5\sqrt{5x}}{5x} \\ =\frac{\sqrt{5x}}{x} \end{gathered}$$