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Understanding and Simplifying Surds | Explained with Examples and Challenges

Explore the concept of surds, square roots that can't be whole numbers, and learn how to manipulate and simplify them. Practice multiplying, dividing, and adding surds with helpful examples and a 2-minute challenge. Get ready to master surds effortlessly!

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Understanding and Simplifying Surds | Explained with Examples and Challenges

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  1. 28/07/10 SURDS • What is a surd? • Manipulating and simplifying surds

  2. 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. √81looks like a surd, but isn't really...

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

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

  5. 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 =

  6. 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

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

  8. 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 =

  9. 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

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

  11. 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

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