Factors, Powers And Standard Form Worksheet Page 7
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2110.3
Squares, cubes and roots
Keywords
square root, positive
Why learn this
Objectives
square root, negative
This topic often
E
Calculate squares and cubes
square root, cube root
comes up in the
E
Calculate square roots and cube roots
exam.
D
Understand the difference between positive and negative
square roots
C
Evaluate expressions involving squares, cubes and roots
Skills check
1 Work out
a 2
b 9
c 4
d 3
2
2
2
2
2 Work out
a 23 3 23
b 26 3 26
c 21 3 21
d 212 3 212
3 What is the largest two-digit square number?
Squares and square roots
To square a number you multiply it by itself.
square
The inverse of squaring is fi nding the square root.
5
25
Every positive number has two square roots. 5 is the positive
square root of 25 and 25 is the negative square root of 25.
square root
5
2
5 5 25
(5)
2
5 5 25
__
You can write the negative
The symbol
0
is used to represent the positive square root
√
square root of 25 as
25.
√
___
of a number. You write
25 5 5.
√
You need to know the squares of integers up to 15 and their corresponding square roots.
Cubes and cube roots
The inverse operation of cubing is fi nding the cube root.
4
3
64
__
3
3
64 4
Every number has exactly one cube root. The symbol
0
√
√
is used to represent the cube root of a number.
You need to know the cubes of 1, 2, 3, 4, 5 and 10 and their corresponding cube roots.
D
Example 6
______
3
√
a
Write down the negative square root of 81.
b
Work out
5
2
1 2 .
C
___
a
81 5 9 so the negative square root of 81 is 29.
(29)
2
5 81
√
_______
________
3
3
√
b
5
2
1 2 5
25 1 2
√
The cube root sign is like a bracket.
___
You have to work out the value
3
27
√
5
underneath the cube root fi rst.
5 3
164
Factors, powers and standard form
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