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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. 235 (page 799)

Simplify:
$(- 4 + \sqrt{17}) (- 3 + \sqrt{17})$

Short Answer

Expert verified

The value of the expression is $29 - 7 \sqrt{17}$

Step by step solution

01

Step 1. Given information

The given expression is $(- 4 + \sqrt{17}) (- 3 + \sqrt{17})$

02

Step 2. Simplifying the expression

Multiplying the terms in the expression using distributive property we get:

$(- 4 + \sqrt{17}) (- 3 + \sqrt{17}) 12 - 4 \sqrt{17} - 3 \sqrt{17} + {(\sqrt{17})}^{2}$

Adding or subtracting the like terms, we get:

$- 4 \sqrt{17} - 3 \sqrt{17} + 12 + 17 - 7 \sqrt{17} + 29 29 - 7 \sqrt{17}$

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Most popular questions from this chapter

In the following exercises, write with a rational exponent.

$(a) \sqrt[5]{u^{2}} (b) (\sqrt[3]{6 x})^{5} (c) \sqrt[4]{{(\frac{18 a}{5 b})}^{7}}$

Simplify:

a. $\frac{m^{\frac{2}{3}} 路 m^{\frac{- 1}{3}}}{m^{\frac{- 5}{3}}}$ b. ${(\frac{25 m^{\frac{1}{6}} n^{\frac{11}{6}}}{m^{\frac{2}{3}} n^{\frac{- 1}{6}}})}^{\frac{1}{2}}$

Use the Quotient Property to simplify square roots.

(a) $\frac{\sqrt{80 q^{5}}}{\sqrt{5 q}}$

(b) $\frac{\sqrt[3]{- 625}}{\sqrt[3]{5}}$

(c) $\frac{\sqrt[4]{80 m^{7}}}{\sqrt[4]{5 m}}$

Use the Quotient Property to simplify square roots.

(a) $\frac{\sqrt{45 p^{9}}}{\sqrt{5 q^{2}}}$

(b) $\frac{\sqrt[4]{64}}{\sqrt[4]{2}}$

(c) $\frac{\sqrt[5]{128 x^{8}}}{\sqrt[5]{2 x^{2}}}$

Use the Quotient Property to simplify square roots.

(a) $\sqrt{\frac{50 r^{5} s^{2}}{128 r^{2} s^{6}}}$

(b) $\sqrt[3]{\frac{24 m^{9} n^{7}}{375 m^{4} n}}$

(c) $\sqrt[4]{\frac{81 m^{2} n^{8}}{256 m n^{2}}}$

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