How to rationalise the denominator of a fraction (surds)

How To Rationalise The Denominator Video

Basically, if you are asked to rationalise the denominator of the fraction you need to get rid of the surd on the bottom of the fraction and make it a whole number. In nearly all cases you can do this by making an equivalent fraction by multiplying it by the surd on the denominator. Let’s go through some worked questions on rationalising the denominator.

Question 1

Make the denominator of this fraction rational (rationalise the denominator):

6/√7

You can rationalise the denominator here by multiplying the numerator and denominator of the fraction by √7.

Multiplying the numerator by √7 gives 6√7

Multiplying the denominator by √7 gives 7

So your rationalised fraction is 6√7/7

Question 2

Make the denominator of this fraction rational (rationalise the denominator):

√5/√6

You can rationalise the denominator here by multiplying the numerator and denominator of the fraction by √6.

Multiplying the numerator by √6 gives √30

Multiplying the denominator by √6 gives 6

So your rationalised fraction is √30/6

Question 3

Make the denominator of this fraction rational (rationalise the denominator):

2√8/3√7

You can rationalise the denominator here by multiplying the numerator and denominator of the fraction by √7 (or 3√7)

Multiplying the numerator by √7 gives 2√56

Multiplying the denominator by √7 gives 21

So your rationalised fraction is 2√56/21

For some extra advice on making the denominator rational try these links:

More examples on rationalising the denominator.

Harder Examples on rationalising the denominator.

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Comments 2 comments

catman3000 profile image

catman3000 6 years ago from England, UK Author

Well noticed Villagepeople. Changes have been made.


VillagePeople 6 years ago from United Kingdom

nice post! I would however adjust 6?7 = 7 in the first question as it is very misleading, perhaps put the numerators on the top to make the equality hold.

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