2. What Goes In The Box ? Rationalise the denominator of the following expressions: Time's up!

3. Rationalising Denominators Aim: To be able to rationalise denominators of the form √a ; (1 + / - √a) or (√a + / - √b) Answer exam questions involving surds and rationalising denominators Know the square numbers up to 15 2 Know the cube numbers up to 6 3

4. Difference of 2 squares. This is a conjugate pair. The brackets are identical apart from the sign in each bracket. Now observe what happens when the brackets are multiplied out: =  3 X  3 - 6  3 + 6  3 - 36 = 3 - 36 = -33 When the brackets are multiplied out the surds cancel out and we end up seeing that the expression is rational. This result is used throughout the following slide.

5. Rationalise the denominator in the expressions below by multiplying top and bottom by the appropriate conjugate: In both of the above examples the surds have been removed from the denominator as required. Quick fire square numbers and cube numbers MWB

6. What Goes In The Box ? Rationalise the denominator in the expressions below : End Extension Rationalise Hence write a process for rationalising a denominator with three surds.

7. Homework Video & Quiz Length and Midpoint of Lines

8. Have a go Make mathematical sentences out of the card sets. See how many you can do? See how complicated you can make them, but must be correct! Mathsnet activities moodle

23. Surds Activities: True or false Exercise Level 2 Make more sentences

24. Harder Surds We met surds when solving quadratic equations. e.g. Find the roots of the equationSolution: Using the formula for : Simplifying the surd:

25. Harder Surds 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.

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

27. Harder Surds 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.

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

29. Harder Surds SUMMARY  To rationalise the denominator of a fraction of the form... multiply the numerator and denominator by