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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset Vaia Explanations$ Math

2nd Edition · 1240 pages

ISBN: 9780998625713

Chapter 9: Q 368 (page 1091)

In the following exercises, simplify by rationalizing the denominator
$\frac{\sqrt{5}}{\sqrt{n} - \sqrt{7}}$

Short Answer

Expert verified

$\frac{\sqrt{5} (\sqrt{n} + \sqrt{7})}{n - 7}$

Step by step solution

01

Step 1. Given information

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

02

Step 2. Rationalize

$\frac{\sqrt{5}}{\sqrt{n} - \sqrt{7}} \frac{\sqrt{5}}{\sqrt{n} - \sqrt{7}} \times \frac{\sqrt{n} + \sqrt{7}}{\sqrt{n} + \sqrt{7}} \frac{\sqrt{5} (\sqrt{n} + \sqrt{7})}{(\sqrt{n} - \sqrt{7}) (\sqrt{n} + \sqrt{7})} \frac{\sqrt{5} (\sqrt{n} + \sqrt{7})}{n - 7}$

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Most popular questions from this chapter

Try It.

Solve: $\sqrt{m} + 5 = \sqrt{m + 16}$

In the following exercises, simplify by rationalizing the denominator

(a) $\frac{3}{3 + \sqrt{11}}$ (b) $\frac{8}{1 - \sqrt{5}}$

In the following exercises, simplify.

$\frac{\sqrt{26 y^{7}}}{\sqrt{2 y}}$

In the following exercises, simplify and rationalize the denominator.

$\sqrt{\frac{19}{175}}$

In the following exercises, solve.

$\sqrt{2 m + 1} + 4 = 0$

See all solutions

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