Rationalising Denominators (AQA GCSE Maths)
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Maths
Rationalising Denominators
What does it mean to rationalise a denominator?
- If a fraction has a surd on the denominator, it is not in its simplest form and must be rationalised
- Rationalising a denominator changes a fraction with surds in the denominator into an equivalent fraction
- The denominator will be an integer and any surds are in the numerator
How do I rationalise the denominator of a surd?
- To rationalise the denominator if the denominator is a surd
- STEP 1: Multiply the top and bottom by the surd on the denominator:
- This ensures we are multiplying by 1; so not affecting the overall value
- STEP 2: Multiply the numerator and denominators together
- so the denominator is no longer a surd
- STEP 3: Simplify your answer if needed
- STEP 1: Multiply the top and bottom by the surd on the denominator:
Exam Tip
- Remember that the aim is to remove the surd from the denominator, so if this doesn't happen you need to check your working or rethink your working
- If a question involving rationalising a denominator appears in a calculator paper, you can use your calculator to check your answer by typing in the un-rationalised fraction - you will still need to show full working though if asked!
Worked example
Write in the form where is a fraction in its simplest form and has no square factors.
There is a surd on the denominator, so the fraction will need to be multiplied by a fraction with this surd on both the numerator and denominator
Multiply the fractions together by multiplying across the numerator and the denominator.
By multiplying out the denominator, you will notice that the surds are removed
Rewriting in the form and simplifying the fraction
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