28/07/10 SURDS What is a surd? Manipulating and simplifying surds.

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Presentation transcript:

28/07/10 SURDS What is a surd? Manipulating and simplifying surds

√81 looks like a surd, but isn't really... SURDS 28/07/10 What is a surd? A surd is a square root which cannot be reduced to a whole number. Examples: √2 is a surd. √5 is a surd. √81 looks like a surd, but isn't really...

SURDS √2 = 1.4142135623730950488... √8 = 2.8284271247461900976... What do you think you get when you multiply these two numbers together?

√2 x √8 = 4 √16 √2 x √18 = 6 √36 √4 x √9 = 2 x 3 = 6 = √36 √3 x √5 = Multiplying Surds What is 4 the square root of? √2 x √8 = 4 √16 What is 6 the square root of? √2 x √18 = 6 √36 √4 x √9 = 2 x 3 = 6 = √36 √3 x √5 = √15 General Rule:

√3 x √12 = √3 x √4 = √2 x √5 = √5 x √5 = √6 x √9 = √5 x √20 = 2-minute challenge: How many can you do? Simplify answers where possible. √3 x √12 = √3 x √4 = √2 x √5 = √5 x √5 = √6 x √9 = √5 x √20 = √3 x √27 = √2 x √3 x √6 =

√3 x √12 = 6 √3 x √4 = √12 √2 x √5 = √10 √5 x √5 = 5 √6 x √9 = √54 2-minute challenge: Answers √3 x √12 = 6 √3 x √4 = √12 √2 x √5 = √10 √5 x √5 = 5 √6 x √9 = √54 √5 x √20 = 10 √3 x √27 = 9 √2 x √3 x √6 = 6

√8 ÷ √2 = 2 √4 √27 ÷ √3 = 3 √9 √36 ÷ √9 = 6 ÷ 3 = 2 = √4 √15 ÷ √5 = √3 Dividing Surds What is 2 the square root of? √8 ÷ √2 = 2 √4 What is 3 the square root of? √27 ÷ √3 = 3 √9 √36 ÷ √9 = 6 ÷ 3 = 2 = √4 √15 ÷ √5 = √3 General Rule:

√12 ÷ √3 = √44 ÷ √4 = √100 ÷ √4 = √25 ÷ √5 = √81 ÷ √9 = √75 ÷ √25 = 2-minute challenge: How many can you do? Simplify answers where possible. √12 ÷ √3 = √44 ÷ √4 = √100 ÷ √4 = √25 ÷ √5 = √81 ÷ √9 = √75 ÷ √25 = √28 ÷ √7 = (√2 x √9) ÷ √3 =

√12 ÷ √3 = 2 √44 ÷ √4 = √11 √100 ÷ √4 = 5 √25 ÷ √5 = √5 √81 ÷ √9 = 3 2-minute challenge: Answers √12 ÷ √3 = 2 √44 ÷ √4 = √11 √100 ÷ √4 = 5 √25 ÷ √5 = √5 √81 ÷ √9 = 3 √75 ÷ √25 = √3 √28 ÷ √7 = 2 (√2 x √9) ÷ √3 = √6

√9 + √16 = ? √(9 + 16) = √25 √9 + √16 = 3 + 4 = 5 = 7 Adding Surds = 5 = 7 There isn't a rule for adding or subtracting! General Rule:

Exam Question (5 - √3)² = (5 - √3)(5 - √3) = 25 - (√3 x 5) – (5 x √3) + (√3 x √3) = 25 - 5√3 – 5√3 + √9 = 25 - 10√3 + 3 = 28 - 10√3