1. Surds Multiplication And DOTs
𝒂+𝒃 𝒄
𝟐 𝟏+ 𝟑
Surds Multiplication
And DOTs

2. Surds – Multiplication
KUS objectives
BAT simplify and rationalise surds
BAT solve equations using the rules for indices and surds
Starter:
𝟏𝟗 𝟏𝟗
𝟐 𝟖
𝟓 𝟏𝟎
𝟑 𝟏𝟖
𝟐 𝟕 𝟐
5 𝟐 × 𝟐

3. 3 25 2 7 3 +2 WB29a Explore making an integer
Multiply each of the given numbers by a single term to give an integer answer 3
25
2 7
3 +2

4. (2 + 3) (2 - 3) = 4 - 23 + 23 - 3 3 = 4 + 0 - 3 = 1
WB29b ‘making an integer
(2 + 3)
(2 - 3)
Multiply by the ‘conjugate’
= 3 + 23 - 3 3 =
= 1
This is the same structure as ‘difference of squares’ for quadratics
Now try these:
(1 + 5)(1 - 5)
(6 + 23)(6 - 23)

5. Practice 1: Rationalise these!3
1 + 3
1 + 23 7
4 + 7
5 + 37 5
5 – 1
25 + 2
23
3 + 4
33 - 6
56
2 - 7
27- 3
105
10 – 4
7 - 35

6. a a = a and (a + b)(a - b) = a2 – b2
Summary Notes: Rationalise a surd
This is a ‘trick’ to make the denominator an integer when you have a surd as a denominator.
First make sure you are happy that
a a = a and (a + b)(a - b) = a2 – b2
11  11 = 11
(7 + 11) (7 - 11)
= 49 – 1111
= 49 – 11
= 38

7. One thing to improve is –
KUS objectives BAT simplify and rationalise surds
BAT solve equations using the rules for indices and surds
self-assess
One thing learned is –
One thing to improve is –

8. END

9. TRIPODS: CHALLENGE X