Help your students prepare for their Maths GCSE with this free rationalise the denominator worksheet of 38 questions and answers
Surds are the square roots of numbers that cannot be simplified. They are used to write irrational numbers precisely for the sake of accuracy in calculations. When surds are written as decimals, they go on forever without any pattern. Irrational numbers cannot be written as fractions with integer numerators and denominators.
Sometimes we might be asked to rationalise the denominator of a fraction. This means finding an equivalent fraction which does not have a surd in the denominator. To rationalise the denominator of a fraction which has one term involving a surd as the denominator, we multiply the numerator and denominator of the fraction by the surd.
To rationalise the denominator when the denominator is made up of a surd and a rational number, we multiply both the numerator and the denominator of the fraction by the conjugate of the denominator. The conjugate is found by changing the sign between the two terms.
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