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Surds

S5 Int2. Surds. Simplifying a Surd. Rationalising a Surd. www.mathsrevision.com. Conjugate Pairs. S5 Int2. Starter Questions. Use a calculator to find the values of : . = 6. = 12. = 2. = 2. The Laws Of Surds. S5 Int2. Learning Intention. Success Criteria.

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Surds

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  1. S5 Int2 Surds Simplifying a Surd Rationalising a Surd www.mathsrevision.com Conjugate Pairs www.mathsrevision.com

  2. S5 Int2 Starter Questions Use a calculator to find the values of : = 6 = 12 = 2 = 2 www.mathsrevision.com

  3. The Laws Of Surds S5 Int2 Learning Intention Success Criteria • To explain what a surd is and to investigate the rules for surds. • Learn rules for surds. • Use rules to simplify surds. www.mathsrevision.com www.mathsrevision.com

  4. S5 Int2 = 12 = 6 What is a Surd The above roots have exact values and are called rational These roots do NOT have exact values and are called irrational OR Surds www.mathsrevision.com

  5. Note : √2 + √3 does not equal √5 Adding & Subtracting Surds S5 Int2 Adding and subtracting a surd such as 2. It can be treated in the same way as an “x” variable in algebra. The following examples will illustrate this point. www.mathsrevision.com

  6. First Rule S5 Int2 Examples List the first 10 square numbers 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 www.mathsrevision.com

  7. Simplifying Square Roots S5 Int2 Some square roots can be broken down into a mixture of integer values and surds. The following examples will illustrate this idea: To simplify 12 we must split 12 into factors with at least one being a square number. 12 = 4 x 3 Now simplify the square root. = 2 3 www.mathsrevision.com

  8. Have a go ! Think square numbers S5 Int2  45  32  72 = 9 x 5 = 16 x 2 = 4 x 18 = 35 = 42 = 2 x 9 x 2 = 2 x 3 x 2 = 62 www.mathsrevision.com

  9. What Goes In The Box ? S5 Int2 Simplify the following square roots: (2)  27 (3)  48 (1)  20 = 25 = 33 = 43 (6)  3200 (4)  75 (5)  4500 = 305 = 402 = 53 www.mathsrevision.com

  10. S5 Int2 Starter Questions Simplify : = 2√5 = 3√2 = ¼ = ¼ www.mathsrevision.com

  11. The Laws Of Surds S5 Int2 Learning Intention Success Criteria • To explain how to rationalise a fractional surd. • Know that √a x √a = a. • 2. To be able to rationalise the numerator or denominator of a fractional surd. www.mathsrevision.com www.mathsrevision.com

  12. Second Rule S5 Int2 Examples www.mathsrevision.com

  13. Rationalising Surds S5 Int2 You may recall from your fraction work that the top line of a fraction is the numerator and the bottom line the denominator. Fractions can contain surds: www.mathsrevision.com

  14. Rationalising Surds S5 Int2 If by using certain maths techniques we remove the surd from either the top or bottom of the fraction then we say we are “rationalising the numerator” or “rationalising the denominator”. Remember the rule This will help us to rationalise a surd fraction www.mathsrevision.com

  15. Rationalising Surds S5 Int2 To rationalise the denominator multiply the top and bottom of the fraction by the square root you are trying to remove: ( 5 x 5 =  25 = 5 ) www.mathsrevision.com

  16. Rationalising Surds S5 Int2 Let’s try this one : Remember multiply top and bottom by root you are trying to remove www.mathsrevision.com

  17. Rationalising Surds S5 Int2 Rationalise the denominator www.mathsrevision.com

  18. What Goes In The Box ? S5 Int2 Rationalise the denominator of the following : www.mathsrevision.com

  19. Conjugate Pairs. S5 Int2 Starter Questions Multiply out : = 3 = 14 = 12- 9 = 3 www.mathsrevision.com

  20. The Laws Of Surds Conjugate Pairs. S5 Int2 Learning Intention Success Criteria • To explain how to use the conjugate pair to rationalise a complex fractional surd. • Know that • (√a + √b)(√a - √b) = a - b • 2. To be able to use the conjugate pair to rationalise complex fractional surd. www.mathsrevision.com www.mathsrevision.com

  21. Looks something like the difference of two squares Rationalising Surds Conjugate Pairs. S5 Int2 Look at the expression : This is a conjugate pair. The brackets are identical apart from the sign in each bracket . Multiplying out the brackets we get : = 5 x 5 - 2 5 + 2 5 - 4 = 5 - 4 = 1 When the brackets are multiplied out the surds ALWAYS cancel out and we end up seeing that the expression is rational ( no root sign ) www.mathsrevision.com

  22. Third Rule Conjugate Pairs. S5 Int2 Examples = 7 – 3 = 4 = 11 – 5 = 6 www.mathsrevision.com

  23. Rationalising Surds Conjugate Pairs. S5 Int2 Rationalise the denominator in the expressions below by multiplying top and bottom by the appropriate conjugate: www.mathsrevision.com

  24. Rationalising Surds Conjugate Pairs. S5 Int2 Rationalise the denominator in the expressions below by multiplying top and bottom by the appropriate conjugate: www.mathsrevision.com

  25. What Goes In The Box S5 Int2 Rationalise the denominator in the expressions below : Rationalise the numerator in the expressions below : www.mathsrevision.com

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