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

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 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

(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’ = 4 - 23 + 23 - 3 3 = 4 + 0 - 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)

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

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

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 –

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TRIPODS: CHALLENGE X