Why do we need to rationalise surds?
In pure surds you need to multiply the top and the bottom by the denominator, so you are affectively multiplying by 1 and get a rational answer. Rationalize 1/ \/3 = multiply top and bottom by \/3 to get: \/3/3 With complex surds or radicals you have to multiply the top and bottom of the surd fraction by the conjugate of the bottom – which is basically like applying the difference of two squares rule to get a rational number. The reason you need to do this is: because, think of it this way – you can divide into a surd but not by a surd. If \/2 is a never ending non-repeating decimal and I want to see how many times it goes into 1, There isn’t really anyway I can do that because I don’t know the factors. But, If I have it in the numerator there is a distinct number of times the rational denominator will go into it.
