Unit 1 Pupil Book 5-7 Math Worksheet Page 3
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10.2 Indices and powers
.2 Indices and powers
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Find square numbers, square roots, cube numbers and cube roots
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Write numbers using index notation
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§
Use the square, square root, cube and cube root keys on a
calculator
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Understand and use the index laws for multiplication and
division of numbers in index form
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§
Use the index laws for positive powers of letters
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When you multiply a number by itself, you are ‘squaring’ it.
2
For example 4
4
4
16. 16 is a square number.
Level 5
§ §
Finding the square root of a number is the inverse, or opposite, of squaring.
___
2
16
4 because 4
16. 4 is a square root of 16.
Level 5
§
§
3
5
is ‘fi ve cubed’ which means 5
5
5
125.
125 is a cube number.
Level 6
§ §
The inverse of cubing is fi nding the cube root.
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3
3
125 is 5 because 5
125. 5 is the cube root of 125.
Level 6
§ §
You can write repeated multiplication of numbers using index notation.
5
2
3
4
4
4
4
4
4
and 3
3
5
5
5
3
5
.
Level 6
§
§
There are special rules (or ‘laws’) for working with numbers written using
Did you know?
Did you know?
index notation.
A 16th-century writer
When multiplying, you add the powers:
suggested that the
2
3
2
3
5
3
3
3
3
.
4th power should be
When dividing, you subtract the powers:
called ‘zenzizenzic’,
8
4
8
4
4
5
5
5
5
.
Level 6
&
Level 7
and the 8th power
Why are the numbers fl oating?
Because they’re in-da-seas!
should be called
‘zenzizenzizenzic’!
Level 5
Without using a calculator, write these squares and square roots.
I can recall the
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___
____
2
2
fi rst twelve
a
64
b
25
c
3
d
11
e
100
___
___
_
square numbers and
2
2
f
9
g
1
h
36
i
7
j
25
their square roots
I can use the
Use the squares you know to mentally calculate these.
squares I know
2
2
2
2
to calculate others
15
15 = 3
5, so 15
= 3
5
= 9
25 = 225
×
×
×
mentally
2
2
2
2
a
14
b
16
c
20
d
21
I can estimate
Estimate these square roots.
the square
Use the square root key on your calculator to check the exact answer.
roots of non-square
__
__
2
2
8
2
= 4 and 3
= 9, so
8 lies between 2 and 3 and is closer to 3.
numbers
__
Estimate:
8 = 2.8.
__
___
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___
a
11
b
17
c
32
d
74
__
3
3
cube
cubed
cube number (e.g. 2
)
cube root (e.g.
8 )
index (indices)
6
Getting things in order
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