Short presentation about how to rationalise radicals

1. Rationalising radicals It is not usual to leave a expression with surds or radicals in the denominator. Rationalising a radical expression is “removing” the radical in the denominator. We are going to do this in 3 different cases:

2. Rationalising radicals Case 1 : The radical in the denominator is a square root. For example: We multiply the numerator and the denominator by that square root. In the example:

3. Rationalising radicals Case 1 :

4. Rationalising radicals Case 1 : Try this exercise now:

5. Rationalising radicals Case 1 : Try this exercise now:

6. Rationalising radicals Case 2 : The radical in the denominator is not a square root. For example:

7. Rationalising radicals Case 2 : The radical in the denominator is not a square root. For example: This a little tricky to solve. We multiply the numerator and the denominator by a power of the radical: the “necessary” power to remove the radical. In the example:

8. Rationalising radicals Case 2 :

9. Rationalising radicals Case 2 : Try this exercise now:

10. Rationalising radicals Case 2 : Try this exercise now:

11. Rationalising radicals Case 3 : The denominator is a sum or subtraction with square roots. For example:

12. Rationalising radicals Case 3 : The denominator is a sum or subtraction with square roots. For example: We multiply the numerator and denominator by the same expression in the denominator but changing the sign.

13. Rationalising radicals Case 3 :

14. Rationalising radicals Case 3 : Try this one now:

15. Rationalising radicals Case 3 : Try this one now:

16. Rationalising radicals New term!!! Conjugate radicals We can say that in the last 2 examples, we multiplied both the numerator and the denominator by the conjugate of the denominator.