# 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 by this Author

- 26
A compound shape is a shape that is made up from other simple shapes. In this article we will be working out the area of a L shape (made up from 2 rectangles). To find the area of a compound shape, follow these simple...

- 0
The density, mass and volume triangle is as follows: So if you wanted to work out the density, you would cover up density in the magic triangle to give: Density = Mass/Volume (since mass is above volume) So if...

- 0
The surface area of a triangular prism can be found in the same way as any other type of prism. All you need to do is calculate the total area of all of the faces. A triangular prism has 5 faces, 3 being rectangular and...

## Comments 2 comments

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.