See Problem 2.

Find each real root.

22. 36 square root of 36
23. 0.25 square root of 0.25
24. − 64 3 negative , cube root of 64 ,
25. − 27 3 cube root of negative 27 end root ,

See Problem 3.

Simplify each radical expression. Use absolute value symbols when needed.

26. 16 x 2 square root of 16 , x squared end root
27. 27 y 6 3 cube root of 27 , y to the sixth end root ,
28. x 20 y 28 4 the fourth , root of x to the twentieth . y to the twenty eighth end root ,
29. 32 y 10 5 the fifth , root of 32 , y to the tenth end root ,

    See Problem 4.

30. Grades In many classes, a passing test grade is 70. Using the formula A = 10 R , eh equals 10 square root of r comma  what raw score would a student need to get a passing grade after her score is adjusted?

B Apply

Find the two real solutions of each equation.

31. x 2 = 100 x squared , equals 100
32. x 4 = 1 x to the fourth , equals 1
33. x 2 = 0.25 x squared , equals , 0.25
34. x 4 = 16 81 x to the fourth , equals , 16 over 81
35. Think About a Plan The radius of a spherical balloon can be expressed as r = 3 V 4 π 3 r equals . cube root of fraction 3 v , over 4 pi end fraction end root ,  inches, where r is the radius and V is the volume of the balloon in cubic inches. If air is pumped to inflate the balloon from 500 cubic inches to 800 cubic inches, by how many inches has the radius of the balloon increased?
    • What was the radius of the balloon originally?
    • What was the radius after inflating the balloon to 800 cubic inches?
    • How can you use the two radii to find the amount of increase?
36. Electricity The voltage V of an audio system's speaker can be represented by V = 4 P , v equals 4 square root of p comma  where P is the power of the speaker. An engineer wants to design a speaker with 400 watts of power. What will the voltage be?
37. Boat Building Boat builders share an old rule of thumb for sailboats. The maximum speed K in knots is 1.35 times the square root of the length L in feet of the boat's waterline.
    1. A customer is planning to order a sailboat with a maximum speed of 12 knots. How long should the waterline be?
    2. How much longer would the waterline have to be to achieve a maximum speed of 15 knots?

Simplify each radical expression. Use absolute value symbols when needed.

38. 0.125 3 cube root of 0.125 ,
39. 8 216 3 cube root of 8 over 216 end root ,
40. 0.0016 4 the fourth , root of 0.0016 ,
41. 1 256 4 the fourth , root of 1 over 256 end root ,
42. 16 c 4 4 the fourth , root of 16 , c to the fourth end root ,
43. Open-Ended Write three radical expressions that simplify to − 2 x 2 . negative 2 , x squared , .
44. Reasoning For what positive integers n is each of the statements true?
    1. If x n = b , x to the n , equals b comma  then x is an nth root of b.
    2. If x n = b , x to the n , equals b comma  then x = b n . x equals , the th , root of b , , .

Is each equation always, sometimes, or never true? Explain your answer.

45. x 4 = x 2 square root of x to the fourth end root , equals , x squared
46. x 6 = x 3 square root of x to the sixth end root , equals , x cubed
47. x 8 3 = x 2 cube root of x to the eighth end root , , equals , x squared
48. x 3 3 = | x | cube root of x cubed end root , , equals absolute value of x ,

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