1. Rationalise Surds

2. When solving quadratic equations, we may obtain surds as the roots.
e.g. Find the roots of the equation
Solution:
Using the formula for :
Simplifying the surd:

3. 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.

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

5. 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.

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

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

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