“Teach A Level Maths” Vol. 1: AS Core Modules 23: Harder Surds © Christine Crisp

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We met surds when solving quadratic equations. e.g. Find the roots of the equation Solution: Using the formula for : Simplifying the surd:

We can also simplify surds which are in the denominators of fractions. e.g.1 Write the expression in the form Solution: Multiply the numerator and the denominator by : A fraction is simplified if there are no surds in the denominator.

e.g.2 Simplify the expression Solution: We first simplify the surd. Multiply the numerator and the denominator by

e.g.3 Write the expression in the form Method: We know that So, By multiplying the expression by the surd has disappeared. However, if we multiply the denominator by we must multiply the numerator by the same amount.

Solution: The process of removing surds from the denominator is called rationalising.

SUMMARY To rationalise the denominator of a fraction of the form . . . multiply the numerator and denominator by

Exercises: Simplify the following by rationalising the denominators: 1. 2. 3.

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We can also surds which are in the denominators of fractions. e.g.1 Write the expression in the form Solution: Multiply the numerator and the denominator by : A fraction is simplified if there are no surds in the denominator.

e.g.2 Simplify the expression Solution: We first simplify the surd. Multiply the numerator and the denominator by

e.g.3 Write the expression in the form Method: We know that So, By multiplying the expression by the surd has disappeared. However, if we multiply the denominator by we must multiply the numerator by the same amount.

Solution: The process of removing surds from the denominator is called rationalising.

SUMMARY To rationalise the denominator of a fraction of the form . . . multiply the numerator and denominator by