Year 11 Surds Worksheets (GCSE) | Printable PDFs
Year 11 Surds worksheets for Year 11 Maths (Key Stage 4, GCSE). Students aged 15-16 learn how to Rationalise the Denominator. Rationalising the denominator means rewriting a fraction so that there are no surds or irrational numbers in the denominator. This is done by multiplying the numerator and denominator by a suitable surd or conjugate to create a rational denominator.
Some students may wish to practice Simplifying Surds, for that see Year 10 Surds Worksheets. Students also decipher between rational and irrational numbers. Rational numbers can be written as a fraction of two integers. For example ¾, -2, 0.125, 0.333....Irrational numbers cannot be written as a fraction of two integers. For example π, √2, √5.
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Rationalising The Denominator
Rational and Irrational Numbers
For more Surds Worksheets, see Year 10 Surds Worksheets
Common Questions about Year 11 Surds
What is a rational number?
A rational number can be written as a fraction of two integers, including terminating and recurring decimals.Why do we rationalise the denominator?
Rationalising the denominator removes surds from the bottom of a fraction, leaving the expression in a standard exact form.What is an irrational number?
An irrational number cannot be written exactly as a fraction of two integers and has a non-terminating, non-recurring decimal expansion.
Year 11 Surds Common Mistakes
Common Mistake 1
Students sometimes think all square roots are irrational. Square roots such as √4 and √9 are rational because they simplify to whole numbers.Common Mistake 2
Students often forget to simplify surds fully. For example, √20 should be simplified to 2√5.Common Mistake 3
Students may rationalise the denominator incorrectly by only multiplying the denominator. Whatever is done to the denominator must also be done to the numerator.
Surds Worksheets - Free Worksheets Above
Rationalise The Denominator (A)
Rational and Irrational Numbers
Rationalise The Denominator (A)