Name: _________________________________________
Date: _________
Algebra 2 - Chapter 6 Review - Radicals, Radical Equations, Rational Exponents, Composing
Functions, Finding the Inverse
Multiple Choice
Identify the choice that best completes the statement or answers the question.
What is a simpler form of the radical expression?
1.
36g 6
3.
A) 36 || g 3 ||
36g 4
C) 6 || g 3 ||
D) 6g 4
B)
C)
20 +
45 −
A) 4
5
B)
6
5
C)
13
D) 5
5
5
5
Simplify.
1
2
4. 16
2
A) 16
B) 4
C)
16
D) 16
2
1
3
14
3
2058 −
6
3
2.8
D) 9
What is the simplest form of the
expression?
3
48 +
A) 4
B)
2.
3
6
3
6
6
3
750
What is the simplest form of the number?
6. −27
A)
B)
C)
D)
5. 49
−1.5
1
343
B) -73.5
1
C)
505
D) -47.5
A)
2
3
9
57
–28
–18
7. What is the solution of
A) x = 0
B) x = 16 and x = 0
C) x = 16
D) x = 16 and x = 1
5x + 1 −
x = 5?
Short Answer
What is a simpler form of the radical expression?
10. The formula for the volume of a cone is
1 2
V =
πr h. Find the radius, to the nearest
3
hundredth, of a cone with a height of 3 in. and a
volume of 12 in.3 .
8.
4
81x 20 y 8
9.
3
27x 15 y 24
Multiply and simplify if possible.
11.
12.
6 ⋅
4
11 ⋅
2
4
13.
3
Ê
7x ÁÁÁÁ
Ë
x −7
ˆ
7 ˜˜˜˜
¯
What is the simplest form of the
expression?
14.
3
15.
3
108a 16 b 9
128a 13 b 6
What is the simplest form of the product?
16.
3
3
7x 7 ⋅
7
17.
7
50x y ⋅
9x 4
6xy
4
What is the simplest form of the quotient?
3
18.
162
3
4
19.
3
20.
2x
2
400
4
90x 18
21.
6x 8 y 9
22.
5x 2 y 4
5
270x 20
3
What is the simplest form of the radical
expression?
5x
23. 2
4
2x + 6
4
2x
24. 3
2a − 6
25. A rope is 150 units long. The rope is cut into
two pieces, so that the lengths of the pieces are
in the ratio 2 :3. What is the length of the longer
piece expressed in simplest radical form?
2a
What is the product of the radical expression?
How can you write the expression with
rationalized denominator?
ˆ2
3 ˜˜˜˜
¯
Ê
26. ÁÁÁÁ −5 −
Ë
28.
Ê
27. ÁÁÁÁ
Ë
ˆÊ
10 ˜˜˜˜ ÁÁÁÁ
¯Ë
2 +
2 −
ˆ
10 ˜˜˜˜
¯
3 −
6
3 +
6
Simplify.
1
29. 20
2
32.
1
⋅ 20
2
Write the radical expression
8
7
in
x 15
exponential form.
1
30. 3
3
1
⋅9
3
What is the solution of the equation?
33.
3
x + 10 − 7 = −5
31. Write the exponential expression 3x 8 in radical
form.
34. −10 +
x + 8 = −4
3
35. ( x + 6 )
43. Let f(x) = 3x − 6 and g(x) = x − 2. Find
= 8
5
f
and
g
its domain.
4
36. 4(3 − x)
3
− 5 = 59
44. Let f(x) = x 2 − 16 and g(x) = x + 4. Find
f
g
and its domain.
37. The area of a circular trampoline is 112.07
square feet. What is the radius of the trampoline?
Round to the nearest hundredth.
45. Let f(x) = −2x − 7 and g(x) = −4x + 3. Find
(f û g)(−5).
What is the solution of the equation?
Eliminate any extraneous solutions.
1
38. ( −2x + 6 )
39.
5
1
= ( −8 + 10x)
5
46. Let f(x) = x 2 + 6 and g(x) =
ÊÁ g û f ˆ˜ ( −7 ) .
Ë
¯
x+8
. Find
x
3x + 28 − 8 = x
47. Is relation t a function? Is the inverse of
relations t a function?
Relation t
40. Let f(x) = −5x − 4 and g(x) = 6x − 7. Find f(x)
+ g(x).
41. Let f(x) = 4x − 5 and g(x) = 6x − 3. Find f(x) −
g(x).
x
0
2
4
6
y
–8
–7
–4
–4
What is the inverse of the given relation?
48. y = 7x 2 − 3.
42. Let f(x) = 3x + 2 and g(x) = 7x + 6. Find f ⋅ g
and its domain.
49. y = 3x + 9
50. For the function f(x) = x + 9, find (f û f −1 )(5).
ID: A
Algebra 2 - Chapter 6 Review - Radicals, Radical Equations, Rational Exponents, Composing
Functions, Finding the Inverse
Answer Section
MULTIPLE CHOICE
1.
2.
3.
4.
5.
6.
7.
C
A
A
B
A
A
C
SHORT ANSWER
8. 3 |x 5 |y 2
9. 3x 5 y 8
10. 1.95 in.
11. 2
12.
3
4
33
13. x
7 − 49
3
14. 4a 4 b 2
15. 3a 5 b 3
3
16. x 3 ⋅
4
17. 10x y
18. 3
19. 2
3
4
20. 3x 6
63x 2
5
3
2x
5x
30y
5
4
24. −3
25. 3
3y
5
x3 y2
23. 8
4a
3
21. 3x 8
22.
2a
3
2x
2a
6 units
26. 28 + 10
27. –8
28. −3 + 2
3
2
x
ID: A
29. 20
30. 3
31. 3
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
44.
45.
46.
47.
8
x3
−
15
8x 7
–6
28
26
–5, 11
5.97 feet
7
6
–4
x – 11
–2x – 2
21x 2 + 32x + 12; all real numbers
3; all real numbers except x = 2
x − 4; all real numbers except x ≠ −4
–53
63
55
Relation t is a function. The inverse of relation t is not a function.
48. y = ±
49. y =
50. 5
x+3
7
1
x−3
3