 # Rationalising Denominators (1)

In this worksheet, students rationalise the denominator of a fraction, giving answers as surds if necessary. Key stage:  KS 4

Curriculum topic:  Number

Curriculum subtopic:  Calculate Exactly with Fractions and Multiples of Pi

Difficulty level:   ### 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

 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
(√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
(√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
(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
√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
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
(√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
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
(√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
(√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
2(√21)/3
EDDIE SAYS
Multiply top and bottom by √15
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