1. 𝒂+𝒃 𝒄
𝟐 𝟏+ 𝟑
Surds + Pythagoras

2. Where a, b and c are rational numbers
Definition: SURD FORM
Where a, b and c are rational numbers

3. starter
SURDS are… are not…
Use to define surds

4. ab = a b and a/b = a/b
Notes: Reminder:
ab = a b and a/b = a/b
for example:

5. 𝟒 𝟐 𝟖 𝟑 𝟐 𝟒 + 𝟐 𝟐 𝟐 𝟐 + 𝟑 𝟖 Surds Simplify KUS objectives
BAT simplify Surds in different types of problems
Simplify
𝟒 𝟐 𝟖
𝟑 𝟐 𝟒 + 𝟐 𝟐
𝟐 𝟐 + 𝟑 𝟖

6. Draw a line with a length of exactly √5 units
Challenge
Draw a line with a length of exactly √5 units A C B
Click for a hint:

7. 4 6 A C B BC2 = 62 + 42 BC =  52 BC =  4   13 BC = 2  13
WB22 Pythagoras reminder
Find length BC and express your
answer as an exact simplified value
BC2 =
BC =  52
BC =  4   13
BC = 2  13

8. C B WB 23 Pythagoras B is (11 , 6) C is ( 1.5, 10) and D is (-2, 3)
Show that length BC is
Show that length CD is

9. WB 24a E F D A B C
2 7
2 5
Write the lengths of AB and DF in the form 𝑘 3
[3]

10. WB 24b – find the missing length and give the answer as a simplified surd (all triangles are RATS)6 8 ? 11 F ? D A C 5 ? J K
Answers
(5x5+ 5x5) =  50 = 25 2 = 5 2
(4x4+ 2x2) =  20 = 4 5 = 2 5
(8x8 - 6x6) =  28 =  4 7 = 2 7
(12x x8) =  80 = 16 5 = 4 5
More qs like this on Khan academy: Pythagoras H 50 30 48 ? G I L 5

11. Height triangle = Area triangle =
Pythagoras problem:
WB 25a What is the exact area of the triangle?
Height triangle =
Area triangle =

12. WB 25b Try these (find the area):
Ans: 6
Ans: 4
Ans: 21
Ans: 7.5

13. One thing to improve is –
KUS objectives BAT
self-assess
One thing learned is –
One thing to improve is –

14. END

15. Practice
Ex 1A
HWK 1B