The smart way to improve grades

Comprehensive & curriculum aligned

Affordable pricing from £10/month

Rationalising Denominators (1)

In this worksheet, students rationalise the denominator of a fraction, giving answers as surds if necessary.

'Rationalising Denominators (1)' worksheet

Key stage:  KS 4

Curriculum topic:  Number

Curriculum subtopic:  Calculate Exactly with Fractions and Multiples of Pi

Difficulty level:  

down

Worksheet Overview

QUESTION 1 of 10

When we rationalise the denominator of a fraction that contains roots, we aim to remove the surd from the bottom of the fraction.

Remember that

√a x √a = √aa = √ =a


 

Example

Rationalise the denominator of this fraction giving your answer as a surd in the form a√b, where a and b are integers and b is as small as possible, or if the answer is a whole number, just state the whole number.

 

3
√6


Answer 

3
√6

 

Multiply top and bottom by √6 to get

 

3√6
√6√6

 

This simplifies to

 

3√6
√36

 

which simplifies to

 

3√6
6

 

which simplifies to

 

√6
2


or ½√6

Rationalise the denominator of this fraction giving your answer as a surd in the form a√b, where a and b are integers and b is as small as possible, or if the answer is a whole number, just state the whole number.

 

1
√6
6√6

(√6)/6

36

Rationalise the denominator of this fraction giving your answer as a surd in the form a√b, where a and b are integers and b is as small as possible, or if the answer is a whole number, just state the whole number.

 

1
√5
5√25

(√5)/5

5

Rationalise the denominator of this fraction giving your answer as a surd in the form a√b, where a and b are integers and b is as small as possible, or if the answer is a whole number, just state the whole number.

 

2
√3
5√25

(√5)/5

(2√3)/3

Rationalise the denominator of this fraction giving your answer as a surd in the form a√b, where a and b are integers and b is as small as possible, or if the answer is a whole number, just state the whole number.

 

3
√3
√3

(√3)/3

(√9)/3

Rationalise the denominator of this fraction giving your answer as a surd in the form a√b, where a and b are integers and b is as small as possible, or if the answer is a whole number, just state the whole number.

 

6
√3
2√3

(√3)/3

(√9)/3

Rationalise the denominator of this fraction giving your answer as a surd in the form a√b, where a and b are integers and b is as small as possible, or if the answer is a whole number, just state the whole number.

 

2
√6
2√3

(√6)/3

(√3)/6

Rationalise the denominator of this fraction giving your answer as a surd in the form a√b, where a and b are integers and b is as small as possible, or if the answer is a whole number, just state the whole number.

 

2
√9
2/3

(√9)/3

(√9)/2

Rationalise the denominator of this fraction giving your answer as a surd in the form a√b, where a and b are integers and b is as small as possible, or if the answer is a whole number, just state the whole number.

 

1
√15
5√3

(√5)/3

(√15)/15

Rationalise the denominator of this fraction giving your answer as a surd in the form a√b, where a and b are integers and b is as small as possible, or if the answer is a whole number, just state the whole number.

 

5
√15
5√3

(√15)/3

(√15)/15

Rationalise the denominator of this fraction giving your answer as a surd in the form a√b, where a and b are integers and b is as small as possible, or if the answer is a whole number, just state the whole number.

 

14
√21
2(√21)/3

(√21)/3

(√21)/21

  • Question 1

Rationalise the denominator of this fraction giving your answer as a surd in the form a√b, where a and b are integers and b is as small as possible, or if the answer is a whole number, just state the whole number.

 

1
√6
CORRECT ANSWER
(√6)/6
EDDIE SAYS
Multiply top and bottom by √6
  • Question 2

Rationalise the denominator of this fraction giving your answer as a surd in the form a√b, where a and b are integers and b is as small as possible, or if the answer is a whole number, just state the whole number.

 

1
√5
CORRECT ANSWER
(√5)/5
EDDIE SAYS
Multiply top and bottom by √5
  • Question 3

Rationalise the denominator of this fraction giving your answer as a surd in the form a√b, where a and b are integers and b is as small as possible, or if the answer is a whole number, just state the whole number.

 

2
√3
CORRECT ANSWER
(2√3)/3
EDDIE SAYS
Multiply top and bottom by √3
  • Question 4

Rationalise the denominator of this fraction giving your answer as a surd in the form a√b, where a and b are integers and b is as small as possible, or if the answer is a whole number, just state the whole number.

 

3
√3
CORRECT ANSWER
√3
EDDIE SAYS
Multiply top and bottom by √3
  • Question 5

Rationalise the denominator of this fraction giving your answer as a surd in the form a√b, where a and b are integers and b is as small as possible, or if the answer is a whole number, just state the whole number.

 

6
√3
CORRECT ANSWER
2√3
EDDIE SAYS
Multiply top and bottom by √3
  • Question 6

Rationalise the denominator of this fraction giving your answer as a surd in the form a√b, where a and b are integers and b is as small as possible, or if the answer is a whole number, just state the whole number.

 

2
√6
CORRECT ANSWER
(√6)/3
EDDIE SAYS
Multiply top and bottom by √6
  • Question 7

Rationalise the denominator of this fraction giving your answer as a surd in the form a√b, where a and b are integers and b is as small as possible, or if the answer is a whole number, just state the whole number.

 

2
√9
CORRECT ANSWER
2/3
EDDIE SAYS
√9 = 3
  • Question 8

Rationalise the denominator of this fraction giving your answer as a surd in the form a√b, where a and b are integers and b is as small as possible, or if the answer is a whole number, just state the whole number.

 

1
√15
CORRECT ANSWER
(√15)/15
EDDIE SAYS
Multiply top and bottom by √15
  • Question 9

Rationalise the denominator of this fraction giving your answer as a surd in the form a√b, where a and b are integers and b is as small as possible, or if the answer is a whole number, just state the whole number.

 

5
√15
CORRECT ANSWER
(√15)/3
EDDIE SAYS
Multiply top and bottom by √15
  • Question 10

Rationalise the denominator of this fraction giving your answer as a surd in the form a√b, where a and b are integers and b is as small as possible, or if the answer is a whole number, just state the whole number.

 

14
√21
CORRECT ANSWER
2(√21)/3
EDDIE SAYS
Multiply top and bottom by √15
---- OR ----

Sign up for a £1 trial so you can track and measure your child's progress on this activity.

What is EdPlace?

We're your National Curriculum aligned online education content provider helping each child succeed in English, maths and science from year 1 to GCSE. With an EdPlace account you’ll be able to track and measure progress, helping each child achieve their best. We build confidence and attainment by personalising each child’s learning at a level that suits them.

Start your £1 trial

Start your trial for £1