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Surds - National 5 Maths Revision
14/10/2022
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A surd is an have e.g. √2 and √25 = 5 have Rules: an √a x √b = Jab = 15 x 2 : 30 Nat S Maths Revision Surds square root (or cube root etc.) which does not answer. a exact = 1.414213... so √2 is a Ja and √25 are so exact Example 1: Simplify 3√2 x 5√2 3√2 x 5√2 = 3 x 5 x √Z x √Z Example 3: Write as a Step 2: add + take away Step 1: (simplify all 3 surds) answer. because √2x √2 =2 6/19 single surd in its √63+√7 = √9×7 + √ Jug =√16x3 =√16 √3 - : = 4√3 Surd. not x 4x√3 Example 2: Express √48 and Jag in their simplest form : (3 √7)+√7-(2 x = 3√7 + √√7 28 √4x7 3√7 +√7 - 2√7 = 2√7 However √a = 3 because they surds simplest form : √63 + √7 -√28 2√7 √x x √x =x x √7) 98 = √2x49 = √2 x √49 = √2 x 7 = 7√2 Note: You can add or take only away the surd sign is the same. √5 + √√3 # 58. Instead the underneath e.g. because simplifying is not possible Rationalising the Denominator bottom of the the fraction the same. Rationalising the denominator means turning the surd at the whole number, whilst keeping 4x√5 √5x√5 Example 1: Express with a rational 1 x√2 3√2 x√2 We do mis not good to The method is very simple: multiply top and bottom by the surd. 6 0/400 Example 2: Express with a rational √8 fraction into Example 3: Express with a *√√√8 *√ 8 because have 11 = 4√3 5 : √2 3x2 6√8 = 8 rational 3√8 4 = a for various mathematical reasons, on me bottom of a surd denominator √2 6 surds answer is left as '√5 + √3 denominator : 312 This when denominator : √8 the number can Simplified be it is fraction.
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