Chapter 9: Q 365 (page 1091)

In the following exercises, simplify by rationalizing the denominator
(a) $\frac{5}{5 + \sqrt{6}}$ (b) $\frac{6}{3 - \sqrt{7}}$

Short Answer

Expert verified

(a) $\frac{5 (5 - \sqrt{6})}{19}$

(b) $3 (3 + \sqrt{7})$

Step by step solution

Step 1. Given Information

(a) $\frac{5}{5 + \sqrt{6}}$ (b) $\frac{6}{3 - \sqrt{7}}$

Part (a) of Step 1. Rationalize.

$\frac{5}{5 + \sqrt{6}} \frac{5}{5 + \sqrt{6}} \times \frac{5 - \sqrt{6}}{5 - \sqrt{6}} \frac{5 (5 - \sqrt{6})}{(5 + \sqrt{6}) (5 - \sqrt{6})} \frac{5 (5 - \sqrt{6})}{19}$

Part (b) of Step 1. Rationalize

$\frac{6}{3 - \sqrt{7}} \frac{6}{3 - \sqrt{7}} \times \frac{3 + \sqrt{7}}{3 + \sqrt{7}} \frac{6 (3 + \sqrt{7})}{(3 - \sqrt{7}) (3 + \sqrt{7})} \frac{6 (3 + \sqrt{7})}{2} 3 (3 + \sqrt{7})$

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In the following exercises, simplify by rationalizing the denominator
(a) $\frac{5}{5 + \sqrt{6}}$ (b) $\frac{6}{3 - \sqrt{7}}$

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)55+6 (b)63-7

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

Theoretical and Mathematical Physics

Calculus

Probability and Statistics

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Study anywhere. Anytime. Across all devices.

In the following exercises, simplify by rationalizing the denominator
(a) $\frac{5}{5 + \sqrt{6}}$ (b) $\frac{6}{3 - \sqrt{7}}$