Intermediate Algebra (11th edition)

SUMMARY EXERCISES on Operations with Radicals and Rational Exponents

7. 8. 9.

10. 11. 12.

13. 14. 15.

16. 17. 18.

19. 20. 21.

22. 23. 24.

25. 26. 27.

28. 29. 30.

31. 32.

Students often have trouble distinguishing between the following two types of problems:

Simplifying a Radical Involving Solving an Equation Using
a Square Root Square Roots

Exercise:Simplify Exercise:Solve
Answer: 5 Answer:

In this situation, represents the
positive square root of 25, namely 5.

225

5 - 5, 5 6

225. x^2 =25.

2316 x^2 - 2354 x^2 + 23128 x^2 A 1 - 233 BA 1 + 233 + 239 B

4 1/2+ 3 1/2

4 1/2- 3 1/2

a 1125 x^32 - 2/3

x3/4y2/3

x1/3y5/8

b

24

x-2/3y4/5

x-5/3y-2/5

212 - 2108 - 2327

B

3

x^2 y

x-^3 y^4

1

1 - 233

6

243

23 + 27

26 - 25

B

3

13

81

A 5 - 323 B

2

212 x- 275 x

26 + 25

26 - 25

- 10

2310

2225

8250

1623

B 5212

3

5 x

3

25 + 2

15

239

xZ 5 238 a^3 b^5 c^9

1

2 x- 25

,

A 25 + 72 A 25 - 7 B

1 - 22

1 + 22

8

27 + 25

In this situation, has two solutions,

the negative square root of 25 or the positive

square root of 25: -5, 5.

x^2 = 25

In Exercises 33– 40, provide the appropriate responses.

33. (a)Simplify

(b)Solve

34. (a)Simplify
    (b)Solve x^2 =100.

2100.

x^2 =64.

264.

35. (a)Solve

(b)Simplify

36. (a)Solve
    (b)Simplify - 225.

x^2 =25.

• 
  
  
  
  216. 
       
  
  
  
  

x^2 =16.

37. (a)Simplify

(b)Solve

38. (a)Simplify

(b)Solve x^2 = 10049.

- 210049.

x^2 = 12181.

- 212181.

39. (a)Solve

(b)Simplify

40. (a)Solve
    (b)Simplify 2 0.09.

x^2 =0.09.

2 0.04.

x^2 =0.04.