Rationalising the denominator (Surds)

  • Google+ icon
  • LinkedIn icon
  • 1736 views

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.

Galen Y. GCSE Chemistry tutor, GCSE Maths tutor, GCSE Biology tutor, ...

About the author

is an online GCSE Maths tutor with MyTutor studying at Imperial College London University

Still stuck? Get one-to-one help from a personally interviewed subject specialist.

95% of our customers rate us

Browse tutors

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok