Q. 276 - Intermediate Algebra

Question

In the following exercises, simplify.

$\frac{\sqrt{5}}{\sqrt{n}-\sqrt{7}}$

Step-by-Step Solution

Answer

The answer is $\frac{\sqrt{5}\left(\sqrt{n}+\sqrt{7}\right)}{n-7}$

Step 1. Given

The expression is $\frac{\sqrt{5}}{\sqrt{n}-\sqrt{7}}$

Step 2. Rationalize the denominators of the given expressions.

$$\begin{gathered} \frac{\sqrt{5}}{\sqrt{n}-\sqrt{7}} \\ =\frac{\sqrt{5}}{\sqrt{n}-\sqrt{7}}\times \frac{\sqrt{n}+\sqrt{7}}{\sqrt{n}+\sqrt{7}} \\ =\frac{\sqrt{5}\left(\sqrt{n}+\sqrt{7}\right)}{{\left(\sqrt{n}\right)}^2-{\left(\sqrt{7}\right)}^2} \\ =\frac{\sqrt{5}\left(\sqrt{n}+\sqrt{7}\right)}{n-7} \end{gathered}$$