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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 9.143 (page 1088)

Simplify.
$\frac{\sqrt{5}}{\sqrt{x} + \sqrt{2}}$

Short Answer

Expert verified

Answer is $\begin{array}{rcl} \frac{\sqrt{5 x} - \sqrt{10}}{x - 2} \end{array}$

Step by step solution

01

Step 1. Given information

Fraction is $\frac{\sqrt{5}}{\sqrt{x} + \sqrt{2}}$ .

02

Step 2. Explanation

$\begin{array}{rcl} \frac{\sqrt{5}}{\sqrt{x} + \sqrt{2}} & = & \frac{\sqrt{5} (\sqrt{x} - \sqrt{2})}{(\sqrt{x} + \sqrt{2}) (\sqrt{x} - \sqrt{2})} \\ = & \frac{\sqrt{5 x} - \sqrt{10}}{x - 2} \end{array}$

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Most popular questions from this chapter

Explain why an equation of the form $\sqrt{x} + 1 = 0$ has no solution.

In the following exercises, simplify by rationalizing the denominator

(a) $\frac{4}{4 + \sqrt{7}}$ (b) $\frac{7}{2 - \sqrt{6}}$

In the following exercises, simplify and rationalize the denominator.

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

Accident investigation: An accident investigator measured the skid marks of one of the vehicles involved in an accident. The length of the skid marks was 175 feet. Use the formula $s = \sqrt{24 d}$ to find the speed of the vehicle before the brakes were applied. Round your answer to the nearest tenth.

Solve: $\sqrt{10 z + 1} - 2 = 0$

See all solutions

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