Chapter 9: Q 364 (page 1091)

In the following exercises, simplify by rationalizing the denominator
(a) $\frac{4}{4 + \sqrt{7}}$ (b) $\frac{7}{2 - \sqrt{6}}$

Short Answer

Expert verified

(a) $\frac{4 (4 - \sqrt{7})}{9}$

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

Step by step solution

Step 1. Given Information

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

Part (a) of Step 1. Rationalize

$\frac{4}{4 + \sqrt{7}} \frac{4}{4 + \sqrt{7}} \times \frac{4 - \sqrt{7}}{4 - \sqrt{7}} \frac{4 (4 - \sqrt{7})}{(4 + \sqrt{7}) (4 - \sqrt{7})} \frac{4 (4 - \sqrt{7})}{9}$

Part (b) of Step 1. Rationalize

$\frac{7}{2 - \sqrt{6}} \frac{7}{2 - \sqrt{6}} \times \frac{2 + \sqrt{6}}{2 + \sqrt{6}} \frac{7 (2 + \sqrt{6})}{(2 - \sqrt{6}) (2 + \sqrt{6})} - \frac{7 (2 + \sqrt{6})}{2}$

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In the following exercises, simplify by rationalizing the denominator
(a) $\frac{4}{4 + \sqrt{7}}$ (b) $\frac{7}{2 - \sqrt{6}}$

Short Answer

Step by step solution

Step 1. Given Information

Part (a) of Step 1. Rationalize

Part (b) of Step 1. Rationalize

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In the following exercises, simplify by rationalizing the denominator(a)44+7 (b)72-6

Short Answer

Step by step solution

Step 1. Given Information

Part (a) of Step 1. Rationalize

Part (b) of Step 1. Rationalize

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Logic and Functions

Geometry

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Statistics

Study anywhere. Anytime. Across all devices.

In the following exercises, simplify by rationalizing the denominator
(a) $\frac{4}{4 + \sqrt{7}}$ (b) $\frac{7}{2 - \sqrt{6}}$