Surds, and other roots - Math Centre

ExampleRationalisetheexpression1√5 −√3.SolutionTorationalisethis,wemustmultiplyitbyafractionwhichequals1.Tochooseasuitablefraction,wethinkofthedifferenceoftwosquares. Asourexpressionhas √ 5 − √ 3inthedenominator,thefractiontouseis ( √ 5 + √ 3)over ( √ 5 + √ 3):1√5 −√3=====√ √1 5 + 3√ √ × √ √5 − 3 5 + 3√ √5 + 3( √ 5 − √ 3)( √ 5 + √ 3)√ √5 + 3( √ 5) 2 − ( √ 3)√ √ 25 + 3√2√5 32 + 2 .Key PointAsurdexpressionintheform1( √ a + √ b)or1( √ a − √ b)canbewrittenas c √ a + d √ bbyusingtheformulaforthedifferenceoftwosquares.Exercises1.Simplifythefollowingexpressions:(a)√40 ×√200 (b)√90 ×√600000 (c)√1000/√40 (d) (1 −√5)(1 +√5)(e) ( √ 7 + 3)( √ 7 − 3)2.Rationalisethefollowingexpressions:(a) 1/ √ 11 (b) 30/ √ 3 (c) 1/(1 − √ 3) (d) 1/( √ 7 + √ 2) (e) 2/( √ 5 − √ 7)Answersc○mathcentreJune23,2009 www.mathcentre.ac.uk 8 mc-TY-surds-2009-1