Rationalising denominator
 2-√3In this case multiplying the bottom and top by √3wouldn't work as we would still get surd at the bottomTo rationalise denominator we have to multiply the topand the bottom of the fraction by 2+√3.√3Rationalise the denominator of Example 1:2-√3√3x(2+√3)x(2+√3)x√3x√3==(2-√3)(2+√3)(2-√3) x √3√3 x √3√3(2+√3)==4+2√3-2√3-32√3-332√3+3It's not good as we stillhave surd in denominator,so we have to multiply bydifferent thing to get rid ofthe surd in denominator.2-√3√3=2√3+3 1+√21-√2In the denominator we have 1+√2, so we have tomultiply the top and the bottom of the fraction by1-√2.We always use the two numbers from the bottom, butwe have to change the sign + to - or - to +.Example 2:Rationalise the denominator of x(1-√2)x(1-√2)=(1+√2)(1-√2)(1-√2)(1-√2)=1-√2+√2-21-√2-√2+2=3-2√21+√21-√2-1=-3+2√2 =√5+1Rationalise the denominator of 5-√5+√5-13√x(√5-1)x(√5-1)=(√5+1) -3(√=(√-√√5+1-)3-)=
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