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2. www.maths4scotland.co.uk Higher Mathematics Surds Next

3. Surds Higher Mathematics What are Surds A surd is a square root which cannot be evaluated without approximation.

4. Surds Higher Mathematics What are Surds A surd is an irrational number An irrational number cannot be written as a simple fraction i.e. as It is a non-recurring decimal

5. Surds Higher Mathematics Why are surds of interest A surd is a square root which cannot be evaluated without approximation. These often occur when using Pythagoras’ Theorem Trigonometry Using surds allows us to be EXACT

6. Surds Higher Mathematics Examples of Surds etc. A good rule of thumb is to think of a surd as: Any root that cannot be evaluated as a whole number. For example: is not a surd

7. Surds Higher Mathematics Which of these are surds ? Yes Yes No Yes No

8. Surds Higher Mathematics Rules of surds We can add or subtract surds if they are the same. Just like algebra:

9. Surds Higher Mathematics Examples Simplify

10. Surds Higher Mathematics Rules of surds We can multiply surds Let’s check this out with simple numbers

11. Surds Higher Mathematics Rules of surds We can multiply surds in general Note that this works both ways

12. Surds Higher Mathematics WARNING Let’s check this out with simple numbers

13. Surds Higher Mathematics Examples Simplify

14. Surds Higher Mathematics Rules of surds We can divide surds Let’s check this out with simple numbers

15. Surds Higher Mathematics Rules of surds We can divide surds in general Note that this works both ways

16. Surds Higher Mathematics A useful tip

17. Surds Higher Mathematics Examples Simplify

18. Surds Higher Mathematics Rules

19. Surds Higher Mathematics Applications We can use the rules of surds for simplification Simplify: Look for largest square factor

20. Surds Higher Mathematics Applications We can use the rules of surds for simplification Simplify: Look for largest square factor

21. Surds Higher Mathematics Applications We can use the rules of surds for simplification Simplify: Look for largest square factor

22. Surds Higher Mathematics Applications We can use the rules of surds for simplification Simplify: Look for largest square factor

23. Surds Higher Mathematics Applications We can use the rules of surds for simplification Simplify:

24. Surds Higher Mathematics Applications We can use the rules of surds for simplification Simplify: Use FOIL

25. Surds Higher Mathematics Applications We can use the rules of surds for simplification Simplify: Use FOIL

26. Surds Higher Mathematics Applications Rationalise the denominator and simplify where possible: To get rid the surd – multiply top and bottom by the surd

27. Surds Higher Mathematics Applications Rationalise the denominator and simplify where possible: To get rid the surd – multiply top and bottom by the surd

28. Surds Higher Mathematics Applications Rationalise the denominator and simplify where possible: To get rid the surd – multiply top and bottom by the conjugate conjugate - the same expression with the opposite sign in the middle

29. Surds Higher Mathematics Applications Rationalise the denominator and simplify where possible: To get rid the surd – multiply top and bottom by the conjugate conjugate - the same expression with the opposite sign in the middle

30. C P D www.maths4scotland.co.uk © CPD 2004 Quit

31. THE END