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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 11: Q.409 (page 1069)

In the following exercises, write each expression in terms of i and simplify if possible. $a) \sqrt{- 16} b) \sqrt{- 11} c) \sqrt{- 8}$

Short Answer

Expert verified

The simplified expression are

a) 4 i b) \sqrt{11} i c) 2 \sqrt{2} i

Step by step solution

01

Part (a) Step 1: Given information

We are given an expression $\sqrt{- 16}$

02

Part(a) Step 2: Use the definition of the square root of a negative number

We get, $\sqrt{16} i$

03

Part (a) Step 3: Simplify

On simplifying we get, $4 i$

04

Part (b) Step 1: Given information

We are given an expression $\sqrt{- 11}$

05

Part (b) Step 2: Use the definition of the square root of negative number

We get, $\sqrt{11} i$

06

Part (b) Step 3: Simplify

On simplifying we get $\sqrt{11} i$

07

Part (c) Step 1: Given information

We are given an expression $\sqrt{- 8}$

08

Part(c) Step 2: Use the definition of the square root of negative number

We get, $\sqrt{8} i$

09

Part (c) Step 3: Simplify

On simplifying we get, $2 \sqrt{2} i$

10

Conclusion

The simplifies expression can be given as

$a) 4 i b) \sqrt{11} i c) 2 \sqrt{2} i$

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Most popular questions from this chapter

Use the Quotient Property to simplify square roots.

(a) $\sqrt{\frac{27 p^{2} q}{108 p^{4} q^{3}}}$

(b) $\sqrt[3]{\frac{16 c^{5} d^{7}}{250 c^{2} d^{2}}}$

(c) $\sqrt[6]{\frac{2 m^{9} n^{7}}{128 m^{3} n}}$

Show two different algebraic methods to simplify $4^{\frac{3}{2}}$ . Explain all your steps.

In the following exercises, simplify each expression.

${(y^{4})}^{3} . {(y^{5})}^{2}$

In the following exercises, add or subtract.

$\sqrt{- 75} + \sqrt{- 48}$

In the following exercises, factor each trinomial of the form

$x^{2} + b x y + c y^{2} m^{2} - 64 m n - 65 n^{2}$

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