Rationalise the Denominator

2011 May June Paper 21 Q1

Without using a calculator, express (5+23)22+3(5+23)22+3 in the form p+q3p+q3, where pp and qq are integers.

(5+23)22+3(5+23)22+3
=(25+203+12)(23)(2+3)(23)=(25+203+12)(23)(2+3)(23)
=(37+203)(23)43=(37+203)(23)43
=74373+40360=74373+40360
=14+33=14+33

2014 May june Paper 21 Q2

Without using a calculator, express 6(1+3)26(1+3)2 in the form a+b3a+b3, where aa and bb are integers to be found.

6(1+3)2=6(1+3)2=61+23+3=64+23=32+32323=6331=633

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