Surds

1
Surds
2
What is to be learned?

• What a surd is
• How to simplify surds

3
What is a Surd?

• 5 is not a surd
• v5 is a surd
• But v9 is not a surd

4
Yes or No?

• v25
• No
• v30
• Yes
• v10
• Yes
• v100
• No

5
These Are Not Surds

• v1 v4 v9 v16 v25 v36 v49 v64
• They are SQUARE numbers
• They are vital when simplifying surds

6
Simplifying Surds

• List of square number very handy
• 4 9 16 25 36 49 64 81 100
• Based on Rule va X vb vab
• e.g v10 X v3
• v30
• BUT used in reverse
• e.g v10
• v2 X v5

7
4 9 16 25 36 49 64 81 100

• Ex 1. Simplify v18
• Look for square number that it will divide by
• ? 9
• v18
• v9 X
• 3 X v2
• 3v2

(A factor!)

• v2

8
4 9 16 25 36 49 64 81 100

• Ex.2 Simplify v50
• Square Number 25
• v50
• v25 X v2
• 5 X v2
• 5 v2

9
4 9 16 25 36 49 64 81 100

• Ex.3 Simplify v48
• Square number 4 or.
• 16!
• Always use BIGGEST square number
• v48
• v16 X v3
• 4 X v3
• 4 v3

10
Surds

• When the root of a number does not give an
  exact value
• e.g v10, v14
• v36, v100

are surds
are not
11
Simplifying surds

• Square Numbers are vital
• 4 9 16 25 36 49 64 81 100
• Must find a square number that is a factor of
  surd
• Ex1 v20
• v 4 X v 5
• 2 X v 5
• 2 v 5

divides exactly by
4
12

• 4 9 16 25 36 49 64 81 100
• Ex2 v32
• v 16 X v 2
• 4 X v 2
• 4 v 2

divides exactly by
4
and 16
Use biggest square number
13
You Try then do p7 booklet Ex 4 1a o(Then
book p 206 Q1 and 2 Omit 1d )

• 1. v12 2. v200 3. v32
• v4 X v3 v100 X v2 v16 X v2
• 2 X v3 10 X v2 4 X v2
• 2 v3 10 v2 4 v2

14
More Simplification

• Keep remembering those square numbers!

15
4 9 16 25 36 49 64 81 100

• Ex 1 v3 X v15
• Multiply
• v45
• Simplify
• v9 X v5
• 3 X v5
• 3 v5

(like before!)
16
4 9 16 25 36 49 64 81 100

• Ex. 2 v5 X v10
• v50
• v25 X v2
• 5 X v2
• 5 v2

17
More Difficult Surds

• v3 X v6
• v18
• v9 X v2
• 3v2

18
You Try (Then p207 Q3 and 5a-c)

• 1. v2 X v10 2. v60 X v5 3. v6 X v8
• v20
• v4 X v5
• 2 v5

v48 v16 X v3 4v3
v300 v100 X v3 10 v3