Powers and Roots
Powers
The number 5² is read “five squared” or “five to the second power”.
The 5 is called a base number. The 2 is called an exponent.
Ex. 5³ is “five cubed” or “five to the third”
54
is “five to the fourth”
5
5
is “five to the fifth”
6
5
is “five to the sixth”
The exponent tells you to multiply the base number times itself the
number the exponent indicates.
5² means 5 times itself or 5
● 5 = 25
Note: Please be careful not to confuse this with 5 ● 2
= 5●5●5 = 125
Ex. 5³
24
= 2●2●2●2 = 16
.3
= .3●.3●.3●.3 = .027
2
3
1
2
r²
2
4
2 2
3 3
4
9
1 1 1 1
2 2 2 2
1
16
= r x r
Powers and Roots
Revised @2009 MLC Page 1 of 7
Square Roots
The mathematical symbol for square root is
To find the square root of 25 look for a number that when multiplied by
itself will result in 25. Therefore the square root of 25 is 5 because 5
x 5 is 25. 25 5
Ex.
16
4
9
3
4 2
100
10
49
7
All of these numbers are called “perfect squares” because there is one
whole number (integer) that is the result of finding the square root.
What if you wanted to find the square root of 13?
We suggest you use your calculator. Depending on the make and model
of your calculator, you may have to press the
symbol first then
the number or the number first then the
Ex.
13
3.60551275
37
8
2.82842712 5
325
symbol.
6.08276253
18.0277563 8
Note: Be aware of rounding instructions when you solve a square root.
There is a method for finding non-perfect square roots that you can
find in the MLC (KC-6). You decide if it’s worth your time.
Powers and Roots
Revised @2009 MLC Page 2 of 7
Powers and Roots Practice
1. 23²
1
2.
3
22
4. 3 4
10.
(.15)
8.
(.5) 2
21
2
2
23
52
43
22
6. 2
4
5. .13
7. .05 3
33
3. 52
4
2
9. 123
11.
16
12.
25
13.
49
14.
649
15.
979
16.
581.54
17.
631
18.
.064
19. The square root of 25 is ____________________.
20. Four squared minus 2 cubed is ______________.
Powers and Roots
Revised @2009 MLC Page 3 of 7
21. 6 8
24. 5 2
27.
30.
22
(.12)
14
42
3
32
33
43
56 1
22. 5 3
23. .12 3
25. .13 2
26. 4 5 2 1
28.
34
8
29. (10 2 ) 4
31.
42
6
32. .46 2
33.
32
34.
12
35.
198
36.
78
37.
144
38.
652
39. One fourth cubed is ____________________.
40. Half of the square root of 36 is ______________.
Powers and Roots
Revised @2009 MLC Page 4 of 7
41.
45
42. 18 2
43. .9 2
44. 33
25
45. .15 2
22
46.
3
47.
34
48. (12 2 ) 1
49. 6 2
(.14) 2
51.
(.4) 3
82
52.
4
50.
72
32
41
52
52
23
23
53.
69
54.
56
55.
190
56.
12
57.
784
58.
982
59. Eight to the fourth power is ____________________.
60. Three to the fifth power multiplied by six is ______________.
Powers and Roots
Revised @2009 MLC Page 5 of 7
61. (.23) 2
64.
4
2
7
2
67. .8 3
70.
63
62. 67 2
63. 12 2
65. .019 3
14
66.
7
68. 2 8
43
2
92
33
54
69.
35
6
71. (112 ) 4
72. .000006 2
73.
985
74.
78
75.
.00008
76.
9.89
77.
27.89
78.
9104.6
79. Three cubed to the fourth power is ____________________.
80. Five squared plus three cubed is ______________.
Powers and Roots
Revised @2009 MLC Page 6 of 7
Answer Key
1) 529
2)
OR .33
3) 89
4) 85
5) .001
6)
OR .25
7) .000125 OR
8) .09 OR
9) 1
10) 2
11) 4
12) 5
13) 7
14) 25.475478
15) 31.288976
16) 24.11514
17) 25.119713
18) .0252982
19) 5
20) 8
21) 1,679,616
22) 125
23) .001728
24) 29
25) .0169
26) 2,048
27) .001728
28) 10.125 OR
29) 100,000,000
30) .296296 OR
31)
32)
33)
34)
35)
36)
37)
38)
39)
40)
41)
42)
43)
44)
45)
46)
47)
48)
49)
50)
51)
52)
53)
54)
55)
56)
57)
58)
59)
60)
2.666667 OR
.2116 OR
5.656854
3.464102
14.071247
8.8831761
12
25.534291
OR .015625
3
1,024
324
.81
59
.0225
1.3333333
3,969
144
28
OR .5
.30625 OR
16
8.306624
7.483315
13.784099
3.464102
28
31.336879
4,096
1,458
61)
62)
63)
64)
65)
66)
67)
68)
69)
70)
71)
72)
73)
74)
75)
76)
77)
78)
79)
80)
.0529
4,489
144
784
.000007
.142857 OR
.512 OR
881
40.5 OR
228
214,358,881
.000000000036
31.38471
8.831761
.008944
3.144837
5.281098
95.418028
531,441
52
Powers and Roots
Revised @2009 MLC Page 7 of 7