Surds

1


Surds
Objectives
2


Surds

• Identify factors that are square numbers
• 20
• 32
• 500
• 45
• 72
• 18
• 98
• 80

25
4 5
225
16 2
169
100 5
121
9 5
81
36 2
12
9 2
14
49 2
7
16 5
3


Surds
Irrational number an irrational number is
a number that is not an integer and cannot be
expressed as a fraction.
Surd a surd is a number containing an irrational
root,
4


Surds
Why use surds?
To write an irrational number in surd form is to
write it accurately.
e.g. p is an irrational number, it has an
infinite number of decimal places if you were to
write it on paper as digits, at some point you
would have to round it and then it would stop
being completely accurate.
We can find out whether a number is rational or
irrational by simplifying it as far as possible.
If we have simplified as far as possible and we
are left with a number such as a square root of a
number that is not a natural square number or a
value such as p then we can determine that the
number is irrational
5


Surds
Example
Are these numbers rational or irrational?
irrational because it cannot be simplified to
an integer
rational because it can be simplified to an
integer
p 2
irrational because p is irrational
p 2p
rational because it can be simplified to
1 2
6


Surds
When simplifying surds it is useful to know the
following
2 2 4
Rule 1
Example
Firstly we will look for factors of 98 that are
square numbers
Simplify
49 2 98
Using the rule
7


Surds
8


Surds
Rule 2
Example
using rule 2
Find factor(s) of 96 that are square numbers
6 2 3 so
9


Surds
10


Surds
11


Surds
Rule 3
Example
12


Surds