1. Surds + Simplify

2. You have already completed the bridging booklet
Reminder
You have already completed the bridging booklet
chapter 7 Indices and you will have met Surds
in GCSE mathematics
If you are already fluent in this topic
Use the rules to simplify and ‘rationalise’ with surds
do the workbook questions and check with your teacher
Go on to …

3. 1 𝑥 𝑥 −1 𝑥 −1/2 3 𝑥 Starter: find the matching pair 𝑥 𝑥 −2 𝑥 2 𝑥 1/2
KUS objectives
BAT simplify and rationalise surds
BAT solve equations using the rules for indices and surds
Starter: find the matching pair
𝑥 𝑥 − 𝑥 𝑥 1/2
𝑥 𝑥 1/ 𝑥 3/ 𝑥
1 𝑥 𝑥 − 𝑥 −1/ 𝑥

4. Area puzzle The green shapes are squares. What is the area of
27cm2
The green shapes
are squares.
What is the area of
the rectangle?
12cm2
The answer is Root 12 times root 27
Students can use calculators and aim is to link together the answer with root 144 = 12
i.e. 1227 = 324 = 18 (and extend to this is equivalent to 12 27 = 4 3 3 9 = 2 x 3 x 3 = 18 if appropriate)

5. More Area puzzles Explain your results
What is the area of each rectangle?
6cm2
24cm2
8cm2
18cm2
Explain your results

6. More Area puzzles questions
We have:
Can you give another multiplication of surds that makes 12?

7. Explain this working

8. 𝒂 × 𝒃 = 𝒂𝒃 𝟏𝟐 = 𝟒 𝟑 =𝟐 𝟑 𝒂 𝒃 = 𝒂 𝒃 𝟒𝟗 𝟏𝟔 = 𝟒𝟗 𝟏𝟔 = 𝟕 𝟒 𝒂 × 𝒂 =𝒂 𝟏𝟐𝟎𝟎 =
WB simplify
Rules for square roots
𝒂 × 𝒃 = 𝒂𝒃 𝟏𝟐
= 𝟒 𝟑
=𝟐 𝟑
𝒂 𝒃 = 𝒂 𝒃
𝟒𝟗 𝟏𝟔
= 𝟒𝟗 𝟏𝟔
= 𝟕 𝟒
𝒂 × 𝒂 =𝒂
Try these:
𝟏𝟐𝟎𝟎 =
𝟏𝟏 × 𝟏𝟏 =
𝟓𝟎 + 𝟏𝟖 =
𝟒 𝟗 × 𝟏𝟖 =

9. Practice 1 8
800
53 2
32
77
50
25 5
72
180
72 6
5 √20
7√21
514 7
3 12
5 50

10. Activity
Work in pairs

11. Practice 2
40
32
75
98
300
12

12. ab = a b and a/b = a/b
Notes: reminder. There are two ‘rules’ of square roots
ab = a b and a/b = a/b
for example:

13. 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 –

14. END