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

2. Module C1
"Certain images and/or photos on this presentation are the copyrighted property of JupiterImages and are being used with permission under license. These images and/or photos may not be copied or downloaded without permission from JupiterImages"

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

4. 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.

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

6. 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.

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

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

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

11. The following slides contain repeats of information on earlier slides, shown without colour, so that they can be printed and photocopied.
For most purposes the slides can be printed as “Handouts” with up to 6 slides per sheet.

12. 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.

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

14. 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.

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

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