1 Press Ctrl-A ©G Dear 2010 – Not to be sold/Free to use Rounding Off Stage 6 - Year 11 Mathematic (Preliminary)

2 Addition and Subtraction Like pronumerals, like surds can be added and subtracted. Like Surds for  2 ?   √43√2√6√8 2 2√2 Surds

3 Addition and Subtraction Examples 1. 2√3 + 4√3 =6√ √7 - 8√7 = 4√ √5 - √125 =13√5 - √25x√5 = 13√5 - 5√5 = 8√5 Surds

4 Multiplication Properties √a x √b =√ab a√b x c√d =ac√bd √a x √a =√a 2 = a Surds

5 Multiplication Examples 1. √2 x √3 =√6 2. 3√5 x 2√3 =6√15 3. √5 x √5 =5 Surds

6 Division Properties √a √b = abab Examples √5 √3 1. = 5353 √9 √3 2. = 9393 = √3 Surds

7 Brackets Properties a(b + c) = ab + ac Examples 1. √2(√3 - √2) =√6 - √4 =√ √5(4√3 - 7√2) =8√ √10 Surds

8 Binomials Properties (a + b)(c + d) = ac + ad + bc + bd (a + b)(a - b) = a 2 - b 2 (a ± b) 2 = a 2 ± 2ab + b 2 Binomials Examples (√2+√5)(√3+√7)=√6 +√14+ √15+ √35 (√5+√3)(√5-√3)= = 5-3 = 2 (√2-√3) 2 = = 2 = 5-2√6-2√6 +3 Surds

9 Rationalising Surds Are Irrational Making the denominator rational. Surds

10 Surds - Rationalising Making the denominator rational. 2 √3 x = 2√3 3 a √b x = a√b b Example Rule Surds

11 Surds - Rationalising Rule a √x+√y a(√x-√y) x - y √x-√y x = Example 4 √2-1 4(√2+1) 2-1 √2+1 x = = 4(√2+1) Conjugate Surd Surds