In mathematics, “rationalising” does not mean you give some reason or excuse for something that you know you have done wrong. It means “make it into a rational number”. Why does rationalising the denominator work? This is because on the bottom (denominator) we have a difference-of-squares expression of the form
(a + b)(a – b) which is equal to a2 – b2.
Since squaring “gets rid” of square roots, a2 and b2 will give you rational numbers (whole numbers or fractions), you will end up with a nice number downstairs (on the denominator). Pupils should make sure they have this technique in their repertoire of skills.
* GCE ‘O’ Level Additional Mathematics
* revision for GCE ‘A’ Level H2 Mathematics
* revision for IB Mathematics HL / SL
* other syllabuses that involve surds
* precocious kids who always want to learn more