Presentation on theme: "Surds Simplifying a Surd Rationalising a Surd Conjugate Pairs"— Presentation transcript:
1 Surds Simplifying a Surd Rationalising a Surd Conjugate Pairs S5 Int2Simplifying a SurdRationalising a SurdConjugate Pairs
2 Starter Questions = 6 = 12 = 2 = 2 S5 Int2Use a calculator to find the values of := 6= 12= 2= 2
3 The Laws Of Surds www.mathsrevision.com Learning Intention S5 Int2Learning IntentionSuccess CriteriaTo explain what a surd is and to investigate the rules for surds.Learn rules for surds.Use rules to simplify surds.
4 What is a Surd = 12 = 6 Surds The above roots have exact values S5 Int2= 12= 6The above roots have exact valuesand are called rationalThese roots do NOT have exact valuesand are called irrational ORSurds
5 Adding & Subtracting Surds Note :√2 + √3 does not equal √5Adding & Subtracting SurdsS5 Int2Adding 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.
6 First Rule List the first 10 square numbers S5 Int2ExamplesList the first 10 square numbers1, 4, 9, 16, 25, 36, 49, 64, 81, 100
7 Simplifying Square Roots S5 Int2Some 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 3Now simplify the square root.= 2 3
8 Have a go ! 45 32 72 = 9 x 5 = 16 x 2 = 4 x 18 = 35 = 42 Think square numbersS5 Int2 45 32 72= 9 x 5= 16 x 2= 4 x 18= 35= 42= 2 x 9 x 2= 2 x 3 x 2= 62
9 What Goes In The Box ? Simplify the following square roots: (2) 27 (3) 48(1) 20= 25= 33= 43(6) 3200(4) 75(5) 4500= 53= 305= 402
11 The Laws Of Surds www.mathsrevision.com Learning Intention S5 Int2Learning IntentionSuccess CriteriaTo 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.
13 Rationalising SurdsS5 Int2You 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:
14 Rationalising Surds This will help us to rationalise a surd fraction S5 Int2If 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 ruleThis will help us to rationalise a surd fraction
15 Rationalising SurdsS5 Int2To 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 )
16 Rationalising Surds Let’s try this one : S5 Int2Let’s try this one :Remember multiply top and bottom by root you are trying to remove
17 Rationalising Surds Rationalise the denominator S5 Int2
18 What Goes In The Box ? Rationalise the denominator of the following :
20 The Laws Of Surds www.mathsrevision.com Conjugate Pairs. S5 Int2Learning IntentionSuccess CriteriaTo explain how to use the conjugate pair to rationalise a complex fractional surd.Know that(√a + √b)(√a - √b) = a - b2. To be able to use the conjugate pair to rationalise complex fractional surd.
21 Looks something like the difference of two squares Rationalising SurdsConjugate Pairs.S5 Int2Look 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= 1When the brackets are multiplied out the surds ALWAYS cancel out and we end up seeing that the expression is rational ( no root sign )