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Surds Simplifying a Surd Rationalising a Surd Conjugate Pairs S5 Int2

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

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Learning Intention Success Criteria 1.To explain what a surd is and to investigate the rules for surds. 1.Learn rules for surds. The Laws Of Surds 1.Use rules to simplify surds. S5 Int2

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

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Adding & Subtracting Surds 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. Note : does not equal 5 S5 Int2

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

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

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45 = 9 x 5 = = 16 x 2 = = 4 x 18 = 2 x 9 x 2 = 2 x 3 x 2 = 6 2 Have a go ! Think square numbers S5 Int2

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

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Starter Questions Simplify : = 25= 32 = ¼ S5 Int2

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Learning Intention Success Criteria 1.To explain how to rationalise a fractional surd. 1.Know that a x a = a. The Laws Of Surds 2.To be able to rationalise the numerator or denominator of a fractional surd. S5 Int2

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Second Rule Examples S5 Int2

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Rationalising Surds 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: S5 Int2

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Rationalising Surds 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 S5 Int2

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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 ) Rationalising Surds S5 Int2

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Lets try this one : Remember multiply top and bottom by root you are trying to remove Rationalising Surds S5 Int2

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Rationalising Surds Rationalise the denominator S5 Int2

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What Goes In The Box ? Rationalise the denominator of the following : S5 Int2

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Starter Questions Multiply out : = 3 = 14 = = 3 Conjugate Pairs. S5 Int2

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Learning Intention Success Criteria 1.To explain how to use the conjugate pair to rationalise a complex fractional surd. 1.Know that (a + b)(a - b) = a - b The Laws Of Surds 2.To be able to use the conjugate pair to rationalise complex fractional surd. Conjugate Pairs. S5 Int2

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S5 Int2 Conjugate Pairs. Rationalising Surds 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 - 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 ) Looks something like the difference of two squares

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

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

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

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What Goes In The Box Rationalise the denominator in the expressions below : Rationalise the numerator in the expressions below : S5 Int2

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