Intermediate Algebra (11th edition)

Brain Busters Rationalize each denominator. Assume that all radicals represent real num-

bers and no denominators are 0.

111.The following expression occurs in a certain standard problem in trigonometry.

Show that it simplifies to. Then verify, using a calculator approximation.

112.The following expression occurs in a certain standard problem in trigonometry.

Show that it simplifies to Then verify, using a calculator approximation.

Rationalize the numerator in each expression. Assume that all variables represent positive

real numbers. (Hint: See the Connections boxfollowing Example 6.)

113. 114. 115. 116.

Solve each equation. See Sections 2.1 and 6.5.

117. 
     
     
     
     118. 
          
     
     
     
     


118. 6 x^2 - 7 x= 3 120.x 115 x- 112 =- 2

- 8 x+ 7 = 4 3 x- 7 = 12

PREVIEW EXERCISES

2 p- 32 q

4 q

22 x- 2 y

3 x

225 - 3

2

6 - 23

8

- 2 - 23.

23 + 1

1 - 23

26 - 22

4

1

22

#^23

2

-

1

22

#^1

2

q

25 +q

p

2 p+ 2

5

2 m-n

3

2 x+y

466 CHAPTER 8 Roots, Radicals, and Root Functions

SUMMARY EXERCISES on Operations with Radicals and Rational Exponents

Perform all indicated operations, and express each answer in simplest form with positive

exponents. Assume that all variables represent positive real numbers.

- 3

26

A 325 + 227 B

2

250 - 298 + 272

6210 - 12210 27 A 27 - 22 B A 1 - 23 BA 2 + 26 B

Conditions for a Simplified Radical

1. The radicand has no factor raised to a power greater than or equal to the index.

2. The radicand has no fractions.

3. No denominator contains a radical.

4. Exponents in the radicand and the index of the radical have greatest

common factor 1.