Download squares and roots of numbers

Number
SQUARES AND SQUARE ROOTS OF
NUMBERS
Squares
The square of a number is the number multiplied by itself.
e.g.
The square of 3 is 9, which is 3 x 3
The square of 10 is 100, which is 10 x 10
We can write a small 2 just above and to the right of a number to show
that we want to square it.
32
102
So
means ‘find the square of 3’ or ‘3 squared’
means ’10 squared’
A
Now have a go at these. Work out:
1)
42
2)
62
3)
92
4)
12
5)
82
6)
122
7)
152
8)
202
9)
112
10)
252
We can square any number, not just whole numbers, in the same way.
1.22 =
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e.g.
1.2 x 1.2
=
1.44
B.
Try working these out.
1)
2.52
2)
3.62
3)
1.52
4)
2.82
5)
0.42
6)
0.62
7)
1.12
8)
0.32
9)
1.42
10)
5.52
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Number
SQUARE ROOTS
The square root of a number is the opposite of squaring a number.
e.g.
If the square of 3 is 9 ( which is 3 x 3)
Then the square root of 9 is 3
We can use the sign
to mean square root.
So 9 means ‘the square root of 9’
To find the square root we have to think of a figure, multiplied by itself,
that will give us the number.
e.g.
C.
1)
16 is 4,
because 4 x 4 = 16
9 is 3,
because 3 x 3 = 9
Now have a go at these.
Write down the square roots of these numbers.
25
2)
100
3)
4
4)
36
5) 49
6)
81
7)
64
8)
1
It is not always straightforward to work out the square root of a number.
Sometimes the number is very large, or the square root is not a whole
number.
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Most calculators have a square root sign button. It will have the square root
sign on it.
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Number
D.
Use a calculator to work out the square roots of the
following. Ask a tutor if you are unsure how to use
the square root button.
1)
256
2)
400
3)
900
4)
625
5)
1225
6)
169
7)
225
8)
289
9)
576
10)
961
E.
Now have a go at these. Where you need to, write
your answers to 3 decimal places. The first one is
done for you.
1)
2 = 1.414 to 3 decimal places.
2)
1.44
3)
2.56
4)
9.61
5)
0.25
6)
5
7)
40
8)
20
9)
90
10)
1000
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Check your answers, then discuss with your tutor what you need to
work on next.
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Number
Answers
Square and Square Roots of Numbers
A
B
C
D
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E
1)
16
2)
36
3)
81
4)
1
5)
64
6)
144
7)
225
8)
400
9)
121
10)
625
1)
6.25
2)
12.96
3)
2.25
4)
7.84
5)
0.16
6)
0.36
7)
1.21
8)
0.09
9)
1.96
10)
30.25
1)
5
2)
10
3)
2
4)
6
5)
7
6)
9
7)
8
8)
1
1)
16
2)
20
3)
30
4)
25
5)
35
6)
13
7)
15
8)
17
9)
24
10)
31
2)
1.2
3)
1.6
4)
3.1
5)
0.5
6)
2.236
7)
6.325
8)
4.472
9)
9.487
10)
31.623
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