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Sample Test: Radicals

Module by: Kenny M. Felder. E-mail the author

Summary: This module provides a sample test related to radicals.

Exercise 1

Punch this into your calculator and give the answer rounded to three decimal places. This is the only question on the quiz where I want an answer in the form of an ugly decimal:

69 = 69 =

Exercise 2

Give me an approximate answer for 10 3 10 3 .

Simplify the following problems in #3-#15. Give answers using radicals, not decimals or approximations.

Exercise 3

400 400

Exercise 4

-27 3 -27 3

Exercise 5

3 -27 3 -27

Exercise 6

108 108

Exercise 7

20 - 45 20 - 45

Exercise 8

300 64 300 64

Exercise 9

x 16 x 16

Exercise 10

x 38 5 x 38 5

Exercise 11

98 x 20 y 5 z 98 x 20 y 5 z

Exercise 12

4 x 2 + 9 y 4 4 x 2 + 9 y 4

Exercise 13

( 3 - 2 ) 2 ( 3 - 2 ) 2

Exercise 14

54 2 + 2 54 2 + 2

Exercise 15

something 3 = x + 2 something 3 =x+2. What is the something?

Exercise 16

Rewrite as an exponent equation: x = y n x= y n

Exercise 17

Rewrite as a radical equation: a b = c a b =c

Exercise 18

Rewrite as a logarithm equation: a b = c a b =c

Solve for x x

Exercise 19

3 + x 2 = 5 3 + x 2 =5

Exercise 20

2 x + 1 - x = 1 2 x + 1 - x =1

Exercise 21

3 x + 3 ( x ) - 4 + 8 = 0 3x+ 3 (x)-4+ 8 =0

Exercise 22

x + 2 ( x ) - 2 = 0 x + 2 (x)- 2 =0

Exercise 23

For an object moving in a circle around the origin, whenever it is at the point ( x x, y y), its distance to the center of the circle is given by: r = x 2 + y 2 r= x 2 + y 2

  • a. Solve this equation for xx.
  • b. If y = 2 y=2 and r = 2 1 2 r=2 1 2 , what is x x?

Exercise 24

Graph y = x + 3 y= x +3.

Exercise 25

What are the domain and range of the graph you drew in #24?

Extra Credit:

Draw a graph of y = x 3 y= x 3 .

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