S4_3_Surds_Ch9 - Surds S4 Credit www.mathsrevision.com...

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www.mathsrevision.com www.mathsrevision.com www.mathsrevision.com Surds Surds Simplifying a Surd Rationalising a Surd S4 Credit
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www.mathsrevision.com www.mathsrevision.com www.mathsrevision.com 5 .     2 Starter Questions Starter Questions Use a calculator to find the values of :  1.     3 6 = 6 = 12 = 2 = 2 2 .     14 4 3 3 .     8 4 4 .     16 1.4 1 2 .7 6 3 6 .     2 1 S4 Credit
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www.mathsrevision.com www.mathsrevision.com www.mathsrevision.com Learning Intention Learning Intention Success Criteria Success Criteria 1. To explain what a surd is and to  investigate the rules for surds. 1. 1. Learn rules for surds. Learn rules for surds. The Laws Of Surds 1. 1. Use rules to simplify surds. Use rules to simplify surds. S4 Credit
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www.mathsrevision.com Surds Surds N = {natural numbers} = {1, 2, 3, 4, ……….} W = {whole numbers}   = {0, 1, 2, 3, ………. .} Z = {integers}   = {….-2, -1, 0, 1, 2, …. .} Q = {rational numbers} This is the set of all numbers which can be written as fractions or ratios . eg 5 = 5 / 1 -7 = -7 / 1 0.6 = 6 / 10 = 3 / 5 55% = 55 / 100 = 11 / 20 etc We can describe numbers by the following sets: S4 Credit
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www.mathsrevision.com R = {real numbers} This is all possible numbers. If we plotted values on a number line then each of the previous sets would leave gaps but the set of real numbers would give us a solid line. We should also note that N “fits inside” W W “fits inside” Z Z “fits inside” Q Q “fits inside” R Surds Surds S4 Credit
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www.mathsrevision.com Surds Surds Q Z W N When one set can fit inside another we say that it is a subset of the other. The members of R which are not inside Q are called irrational (Surd)   numbers. These cannot be expressed as fractions and include π , 2, 3 5 etc R
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www.mathsrevision.com www.mathsrevision.com www.mathsrevision.com 2 What is a Surd What is a Surd 3 6 = 6 = 12   14 4 1.4 1 2 .7 6 3 2 1 The above roots have exact values  and are called rational These roots do  NOT  have exact values  and are called irrational  OR Surds S4 Credit
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www.mathsrevision.com www.mathsrevision.com www.mathsrevision.com Adding & Subtracting Surds Adding  and  subtracting  a  surd  such  as  2.  It  can  be  treated  in  the 
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S4_3_Surds_Ch9 - Surds S4 Credit www.mathsrevision.com...

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