Download Math 100 Review 4 Use a calculator to approximate the square root

Math 100 Review 4
Use a calculator to approximate the square root to 3 decimal places. Check to see that the approximation is reasonable.
1) 8
Find the cube root.
3
2) 729
3)
3 1
216
Find the root. Assume that all variables represent nonnegative real numbers.
4
4) - 625
Find the cube root.
3 x12
5)
125y6
Simplify. Assume that all variables represent any real number.
5
6) (-2)5
7)
5
x5
Find the root. Assume that all variables represent nonnegative real numbers.
4
8) - 1296x12y8
Simplify. Assume that all variables represent any real number.
4
9) x4
10)
(x - 3)2
Evaluate.
11) If f(x) =
2x + 1, find the value of f(1).
Use radical notation to write the expression. Simplify if possible.
12) -243 1/5
13) (8x9 )1/3
14) (-343x15)1/3
15) 2434/5
1
16) 274/3
Write with positive exponents. Simplify if possible.
17) 64-4/3
Use radical notation to write the expression. Simplify if possible.
18) (3x)3/10
Use the properties of exponents to simplify the expression. Write with positive exponents.
19) (r1/7 · s1/7 )2
20)
y3/4
y1/4
Write with positive exponents. Simplify if possible.
1
21)
x-2/7
Use rational exponents to simplify the following.
6
22) 64x3
Write with positive exponents. Simplify if possible.
23) 243-4/5
Use the product rule to multiply. Assume all variables represent positive real numbers.
24) 175 · 7
25)
3
8m 3 ·
3
27m3
Simplify the radical expression. Assume that all variables represent positive real numbers.
26) 48
Use the quotient rule to divide and simplify.
8x2 y
27)
49
28)
18x9
2x
Simplify the radical expression. Assume that all variables represent positive real numbers.
29) y13
2
30)
5
243 x3 y24
31)
45
32)
56x5 y6
2y4
5
33)
77
5
7
Find the distance between the pair of points.
34) (3, 7) and (-7, -4)
Simplify the radical expression. Assume that all variables represent positive real numbers.
3
35) -27a 11b13
Use the quotient rule to divide and simplify.
3 x2
36)
625
Find the midpoint of the line segment whose endpoints are given.
37) (-3, -3), (0, 4)
Find the distance between the pair of points.
38) (-4, -7) and (7, -5)
Add or subtract. Assume all variables represent positive real numbers.
39) -9 2 - 4 50
Rationalize the denominator and simplify. Assume that all variables represent positive real numbers.
40)
41)
3 4
9
7
3
13
81
42) 4
4x9
43)
3
5- 3
3
44)
7
x+6
45)
2x + 2 = 6
Solve.
Perform the indicated operation. Write the result in the form a + bi.
2
46)
5+i
Find the power of i.
47) i36
48) i51
Perform the indicated operation. Write the result in the form a + bi.
4 + 2i
49)
4 - 7i
Rationalize the numerator and simplify. Assume all variables represent positive real numbers.
6
50)
7x
Perform the indicated operation. Write the result in the form a + bi.
51) (5 + 4i)2
52) (3i)(4i)
53) 3i(9 - 6i)
54) (2 - 7i) - (2 - i)
55) (5 - 7i) + (2 + 3i)
Multiply or divide.
12
56)
-6
57)
-9 ·
-2
Write in terms of i.
58) -4
Solve.
59)
3x + 6 + 4 = 0
4
60)
61)
x-3=
3
x + 21
2x = -3
Rationalize the denominator and simplify. Assume that all variables represent positive real numbers.
2
62)
2-9
5
2
63)
Add or subtract. Assume all variables represent positive real numbers.
3
3
64) 14 2 - 3 54
Multiply, and then simplify if possible. Assume all variables represent positive real numbers.
3
3
65) (6 + 3)(6 - 3)
66) ( 12 + 2)( 12 - 2)
67)
7( 14 +
7)
Add or subtract. Assume all variables represent positive real numbers.
3
68) 5
3
a+
27a
6x2 + 7 96x2 + 6 96x2
69)
Use the quotient rule to divide and simplify.
32
70)
25
Use the product rule to multiply. Assume all variables represent positive real numbers.
5
5
71) 3x4 · 10,000
11x3 ·
72)
11x5
Use rational exponents to write as a single radical expression.
4
y
73)
5
y
74)
5
5·
3
2
5
75)
9
x·
3
x2
Use rational exponents to simplify the following.
8
76) y14z 8
77)
24
y18z 20
Use the properties of exponents to simplify the expression. Write with positive exponents.
(-3x1/5 )4
78)
x5/7
79) y5/9 (y3/9 - 2y2/9 )
Identify the domain and then graph the function.
3
80) f(x) = x - 5
y
10
5
-10
-5
5
10
x
5
10
x
-5
-10
81) f(x) =
x-4
y
10
5
-10
-5
-5
-10
Simplify. Assume that all variables represent any real number.
82) x2 - 4x + 4
6
Find the cube root.
3
83) -27x18y24
7
Answer Key
Testname: MTH100R4SUM2010
1) 2.828
2) 9
1
3)
6
4) -5
x4
5)
5y2
6) -2
7) x
-6x3 y2
x
x-3
3
-3
13) 2x3
14) -7x5
8)
9)
10)
11)
12)
15) 81
16) 81
1
17)
256
10
27x3
2/7
19) r s2/7
20) y1/2
21) x2/7
18)
22) 2x1/2
1
23)
81
24) 35
25) 6m 2
26) 4 3
2x 2y
27)
7
28) 3x4
29) y6 y
5
30) 3y4
x3 y4
31) 3 5
32) 2x2 y 7x
33)
34)
5
11
221 units
3
35) -3a 3 b4 a 2 b
8
Answer Key
Testname: MTH100R4SUM2010
3
36)
x2
3
5 5
37) -
3 1
,
2 2
38) 5 5 units
39) -29 2
3
12
40)
3
41)
42)
3
7
169
13
4
4x3
2x3
3
43)
15 + 3 3
22
44)
- 42 + 7 x
x - 36
45) 17
5
1
46)
i
13 13
47) 1
48) -i
2
36
49)
i
+
65 65
50)
6
42x
51)
52)
53)
54)
55)
56)
57)
9 + 40i
-12
18 + 27i
-6i
7 - 4i
-i 2
-3 2
58) 2i
59) ∅
60) ∅
61) -
27
2
62) -
2 2 + 18
79
63)
10
2
9
Answer Key
Testname: MTH100R4SUM2010
64) 5
3
2
3
65) 36 - 9
66) 8
67) 7 2 + 7
3
68) 8 a
69) 53x 6
4 2
70)
5
5
30,000 x4
72) 11x4
20
73)
y
15
74)
4000
9
75) x7
71)
76) y7/4 z
77) y3/4 z 5/6
78) 81x3/35
79) y8/9 - 2y7/9
80) (-∞, ∞)
y
10
5
-10
-5
5
10
x
5
10
x
-5
-10
81) [0, ∞)
y
10
5
-10
-5
-5
-10
10
Answer Key
Testname: MTH100R4SUM2010
82) x - 2
83) -3x6 y8
11