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1. 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. 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. 3. Rationalising radicals Case 1 :
4. 4. Rationalising radicals Case 1 : Try this exercise now:
5. 5. Rationalising radicals Case 1 : Try this exercise now:
6. 6. Rationalising radicals Case 2 : The radical in the denominator is not a square root. For example:
7. 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. 8. Rationalising radicals Case 2 :
9. 9. Rationalising radicals Case 2 : Try this exercise now:
10. 10. Rationalising radicals Case 2 : Try this exercise now:
11. 11. Rationalising radicals Case 3 : The denominator is a sum or subtraction with square roots. For example:
12. 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. 13. Rationalising radicals Case 3 :
14. 14. Rationalising radicals Case 3 : Try this one now:
15. 15. Rationalising radicals Case 3 : Try this one now:
16. 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.