Rationalising the denominator (Surds)

When asked to rationalise simple Surd (square roots that cannot be reduced to a whole number) fractions in the form a/√b we are aiming to remove the surd in the denominator (bottom).


e.g 1. Rationalise 3/√2 

Answer: We multiply the entire fraction by the denominator √2/√2 (this is equivalent to 1).

Let us first consider what happens to the denominator:

√2 x √2 = 2 (any simple surd multiplied by itself equals the number inside)

The numerator (top) becomes 3 x √2 or 3√2 

So the fraction rationalises to 3√2 / 2,  the surd has now been removed from the denominator.

Typically you will be asked to simplify the fraction which is just asking you to rationalise it. The rationalised fraction can be used more easily in further calculations.

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