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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. 272 (page 811)

In the following exercises, simplify.
$\frac{7}{2 - \sqrt{6}}$

Short Answer

Expert verified

The simplified form is $- \frac{7 (2 + \sqrt{6})}{2}$ .

Step by step solution

01

Step 1. Given information.

The given expression is,

$\frac{7}{2 - \sqrt{6}}$ .

02

Step 2. Simplifying.

Now, to rationalize we will multiply the numerator and denominator by the conjugate of the denominator and simplify.

$\frac{7}{2 - \sqrt{6}} = \frac{7 (2 + \sqrt{6})}{(2 - \sqrt{6}) (2 + \sqrt{6})} = \frac{7 (2 + \sqrt{6})}{2^{4} - {(\sqrt{6})}^{2}} = \frac{7 (2 + \sqrt{6})}{4 - 6} = - \frac{7 (2 + \sqrt{6})}{2}$

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Most popular questions from this chapter

Use the Quotient Property to simplify square roots.

(a) $\sqrt{\frac{75 r^{9}}{s^{8}}}$

(b) $\sqrt[3]{\frac{54 a^{8}}{b^{3}}}$

(c) $\sqrt[4]{\frac{64 c^{5}}{d^{4}}}$

In the following exercises, simplify.

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In the following exercises, simplify using absolute value signs as needed. $\sqrt{125 r^{13}}, \sqrt[3]{108 x^{5}}, \sqrt[4]{48 y^{6}}$

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