Rationalising the denominator

The Maths Habit

  1. Simplify √18.

    3√2

  2. Simplify √80.

    4√5

  3. Simplify 3√12.

    6√3

Which would you rather work out without a calculator?

1 ÷ 1.414 1.414 ÷ 2= 0.707

Work out

  1. √3 × √3

    3

  2. √7 × √7

    7

  3. √11 × √11

    11

  4. (√5)2

    5

Rationalise
Rewrite a fraction so there is no root on the bottom.

What do we multiply the top and the bottom by?

10√5 √5

Rationalise the denominator. 14√7

√7√7area 7
multiply the top and the bottom by the root
14√7×√7√7=14√77
Answer2√7

Rationalise the denominator. 12√6

√6√6area 6
multiply the top and the bottom by the root
12√6×√6√6=12√66
Answer2√6

Rationalise the denominator. 14√7

√7√7area 7
multiply the top and the bottom by the root
14√7×√7√7=14√77
Answer2√7

Rationalise the denominator. 4√6

√6√6area 6
multiply the top and the bottom by the root
4√6×√6√6=4√66
Answer2√63

Rationalising the denominator worksheet, page 1

Answer sheet

  1. Show that 12√6 = 2√6

    12√6 ÷ 6

  2. Rationalise √2√5

    √105

  1. Write 21√7 with a rational denominator.

    3√7

  2. Write 5√10 with a rational denominator, in its simplest form.

    √102

  3. Mo says 18√6 = 3. What has he done wrong? Find the right answer.

    3√6
Exit tickets to print