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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 8: Q. 279 (page 811)

In the following exercises, simplify.
$\frac{\sqrt{r} + \sqrt{5}}{\sqrt{r} - \sqrt{5}}$

Short Answer

Expert verified

The answer is $\frac{{(\sqrt{r} + \sqrt{5})}^{2}}{r - 5}$

Step by step solution

01

Step 1. Given

The expression is $\frac{\sqrt{r} + \sqrt{5}}{\sqrt{r} - \sqrt{5}}$

02

Step 2. Rationalize the denominators of the given expressions.

$\frac{\sqrt{r} + \sqrt{5}}{\sqrt{r} - \sqrt{5}} = \frac{\sqrt{r} + \sqrt{5}}{\sqrt{r} - \sqrt{5}} 脳 \frac{\sqrt{r} + \sqrt{5}}{\sqrt{r} + \sqrt{5}} = \frac{{(\sqrt{r} + \sqrt{5})}^{2}}{{(\sqrt{r})}^{2} - {(\sqrt{5})}^{2}} = \frac{{(\sqrt{r} + \sqrt{5})}^{2}}{r - 5}$

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Most popular questions from this chapter

In the following exercises, use the Product Property to simplify radical expressions a. $\sqrt[4]{32}$ ,b. $\sqrt[5]{64}$

In the following exercises, use the Product Property to simplify radical expressions $\sqrt{675}$

In the following exercises, write with a rational exponent.

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(a) $\sqrt{288}$

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