Download Square roots and cube roots (skill sheet)

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Skillsheet
Square roots and cube roots
Square numbers
42 is read as ‘four squared’ and means 4 times itself. 42 ¼ 4 4 ¼ 16.
16 is called a square number.
Square root
pffi
Square root, written as , is the opposite of ‘squared’.
pffiffiffiffiffiffi
pffiffiffiffiffiffi
16 ¼ 4 because 42 ¼ 16. 16 ¼ 4 is read as ‘the square root of 16 is 4’.
The square root of a number is the positive value which, if squared, gives that number.
Example 1
Evaluate each expression.
a 72
b 112
c
pffiffiffi
9
d
pffiffiffiffiffiffiffiffi
121
Solution
a 72 ¼ 7 7 ¼ 49
b 112 ¼ 11 11 ¼ 121
pffiffiffi
c
9 ¼ 3 (because 3 3 ¼ 9)
pffiffiffiffiffiffiffiffi
d
121 ¼ 11 (because 11 11 ¼ 121)
Cube numbers
83 is read as ‘eight cubed’ and means 8 times itself times itself. 83 ¼ 8 8 8 ¼ 512.
512 is called a cube number.
Cube root
pffi
Cube root, written as 3 , is the opposite of cubed.
p
pffiffiffiffiffiffi
ffiffiffiffiffi
ffi
3
64 ¼ 4 because 43 ¼ 64. 3 64 ¼ 4 is read as ‘the cube root of 64 is 4’.
The cube root of a number is the value which, if cubed, gives that number.
Example 2
Evaluate each expression.
a 33
b 63
c
ffiffiffiffiffiffi
p
3
27
d
ffiffiffi
p
3
1
Solution
a 33 ¼ 3 3 3 ¼ 27
b 63 ¼ 6 6 6 ¼ 216
pffiffiffiffiffiffi
c 3 27 ¼ 3 (because 3 3 3 ¼ 27)
pffiffiffi
d 3 1 ¼ 1 (because 1 1 1 ¼ 1)
© Cengage Learning Australia Pty Ltd 2011
MAT07NASS10016
Number and Algebra: Number and place value
www.nelsonnet.com.au
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Exercise
1 Evaluate each square number.
a 32
b 12
c 102
d 52
e 92
f 22
g 62
h 122
2 Evaluate each cube number.
a 23
b 53
c 93
d 103
e 73
f 43
g 113
h 123
3 Use the above examples and your answers to Questions 1 and 2 to complete this table.
Number, n
Number squared, n2
1
1
2
4
3
9
4
Number cubed, n3
64
5
6
7
8
9
10
100
11
1331
12
4 Use the table in Question 3 to find the value of each square root or cube root.
pffiffiffiffiffiffiffiffi
pffiffiffi
pffiffiffiffiffiffiffiffi
a
144
b
4
c 3 125
pffiffiffi
pffiffiffiffiffiffi
pffiffiffiffiffiffi
e
36
f
81
g
1
p
p
ffiffiffi
p
ffiffiffiffiffiffi
ffiffiffiffiffiffiffiffi
3
3
3
j
8
k
64
i
216
pffiffiffiffiffiffi
p
pffiffiffiffiffiffiffiffi
ffiffiffiffiffiffiffiffiffiffiffi
3
m
100
n
25
o
1331
© Cengage Learning Australia Pty Ltd 2011
MAT07NASS10016
p
ffiffiffiffiffiffiffiffi
3
343
p
ffiffiffiffiffiffiffiffi
h 3 729
pffiffiffiffiffiffi
l
64
pffiffiffiffiffiffi
p
49
d
Number and Algebra: Number and place value
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Answers
1 a 9
b 1
c 100
d 25
f 4
g 36
h 144
b 125
c 729
d 1000
f 64
g 1331
h 1728
b 2
c 5
d 7
e 6
f 9
g 1
h 9
i 6
j 2
k 4
l 8
m 10
n 5
o 11
p 7
e 81
2 a 8
e 343
3
n
n2
n3
1
1
1
2
4
8
3
9
27
4
16
64
5
25
125
6
36
216
7
49
343
8
64
512
9
81
729
10
100
1000
11
121
1331
12
144
1728
4 a 12
© Cengage Learning Australia Pty Ltd 2011
MAT07NASS10016
Number and Algebra: Number and place value
www.nelsonnet.com.au