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Rationalising a two-term denominator

Rationalising a two-term denominator.

  • Keep square roots exact unless the question asks for an approximation.
  • Use square factors to simplify. Only matching root parts can be added or subtracted.
  • To rationalise, multiply top and bottom by the same suitable factor.

Example 1

Simplify fully. Give an exact answer.

Multiply top and bottom by the conjugate. The denominator becomes a difference of squares.Collect like terms and cancel common factors where possible.

Example 2

Simplify fully. Give an exact answer.

Multiply top and bottom by the conjugate. The denominator becomes a difference of squares.Collect like terms and cancel common factors where possible.

Your turn

Question 1

Simplify fully. Give an exact answer.

Check answer
Multiply top and bottom by the conjugate. The denominator becomes a difference of squares.Collect like terms and cancel common factors where possible.
Question 2

Simplify fully. Give an exact answer.

Check answer
Multiply top and bottom by the conjugate. The denominator becomes a difference of squares.Collect like terms and cancel common factors where possible.
Question 3

Simplify fully. Give an exact answer.

Check answer
Multiply top and bottom by the conjugate. The denominator becomes a difference of squares.Collect like terms and cancel common factors where possible.
Question 4

Simplify fully. Give an exact answer.

Check answer
Multiply top and bottom by the conjugate. The denominator becomes a difference of squares.Collect like terms and cancel common factors where possible.
Question 5

Simplify fully. Give an exact answer.

Check answer
Multiply top and bottom by the conjugate. The denominator becomes a difference of squares.Collect like terms and cancel common factors where possible.
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