𝒂+𝒃 𝒄 𝟐 𝟏+ 𝟑 Surds + Pythagoras

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

starter SURDS are… are not… Use to define surds

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

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

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:

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 = 62 + 42 BC =  52 BC =  4   13 BC = 2  13

C B WB 23 Pythagoras B is (11 , 6) C is ( 1.5, 10) and D is (-2, 3) Show that length BC is 5 17 2 Show that length CD is 7 5 2

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]

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 (12x12 - 8x8) =  80 = 16 5 = 4 5 More qs like this on Khan academy: Pythagoras H 50 30 48 ? G I L 5

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

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

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

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Practice Ex 1A HWK 1B