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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. 8.3TI (page 745)

Simplify: $(a) \sqrt{- 169}$ $(b) - \sqrt{81}$

Short Answer

Expert verified

The solutions of (a) is there is no real number and (b) is $- 9$

Step by step solution

01

Part (a). Step 1. Given information

The root: $\sqrt{- 169}$

02

Part (a) Step 2. Calculation

We have,

$\sqrt{- 169} = \sqrt{- 169} is not a real number$

There is no real number whose square is $\sqrt{- 169}$

03

Part (b) Step 1. Given information

The root: $- \sqrt{81}$

04

Part (b) Step 2. Calculation

We have,

$- \sqrt{81} = - 9$

Since, $9^{2} = 81$ and the negative is in front of the radical sign.

Therefore, the solution is $- 9$

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Most popular questions from this chapter

Write with a rational exponent:

(a) $\sqrt{x^{5}}$

(b) ${(\sqrt[4]{3 y})}^{3}$

(c) $\sqrt{{(\frac{2 m}{3 n})}^{5}}$

In the following exercises, use the Product Property to simplify radical expressions $\sqrt{147}$

In the following exercises, simplify.

(a) $- 64^{\frac{3}{2}}$

(b) $- 64^{- \frac{3}{2}}$

(c) ${(- 64)}^{\frac{3}{2}}$

Use the Quotient Property to simplify square roots.

(a) $\frac{\sqrt{72 n^{11}}}{\sqrt{2 n}}$

(b) $\sqrt[3]{\frac{162}{6}}$

(c) $\sqrt[4]{\frac{160 r^{10}}{5 r^{3}}}$

Why is there no real number equal to $\sqrt{- 64}$ ?

See all solutions

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