1. Production by Mr Porter 2009
Revision - Surds 1 2
Production by
Mr Porter
2009

2. Definition :
If p and q are two integers with no common factors and , than a is an irrational number.
Irrational number of the form are called SURDS. 1 2

3. Surd Operations
If a, b, c and d are numbers and a > 0 and b > 0, then
Surds can behave like numbers and/or algebra.

4. Simplifying Surds
To simplify a surd expression, we need to (if possible) write the given surd number as a product a perfect square, n2, and another factor. It is important to use the highest perfect square factor but not essential. If the highest perfect square factor is not used first off, then the process needs to be repeated (sometimes it faster to use a smaller factor).
Generate the perfect square number:
Order 1 2 3 4 5 6 7 8 9 10 n2 12 22 32 42 52 62 72 82 92
102
Value 16 25 36 49 64 81
100
Perfect Squares
Factorise the surd number using the largest perfect square :
18 = 9 x 2
24 = 4 x 6
27 = 9 x 3
48 = 16 x 3
Or any square factor:
72 = 36 x 2
72 = 9 x 8
72 = 4 x 18
72 = 4 x 9 x 2

5. Examples: Simplify the following surds.1 4 9 16 25 36 49 64 81
100
121
144
169
196
225

6. Exercise: Simplify each of the following surds.1 4 9 16 25 36 49 64 81
100
121
144
169
196
225

7. Simplifying Surd Expressions.
Examples: Simplify the following (simplify each surd part first). N2 1 4 9 16 25 36 49 64 81
100
121
144
169
196
225

8. Exercise: Simplify the following.1 4 9 16 25 36 49 64 81
100
121
144
169
196
225

9. Simplifying Surd Expressions.
Examples: Simplify the following

10. Exercise: Simplify each of the following (fraction must have a rational denominator).

11. Using the Distributive Law - Expanding Brackets.
Examples: Expand and simplify the following

12. Exercise: Expand the following (and simplify)
Special cases - (Product of conjugates)
Difference of two squares.

13. Rationalising the Denominator - Using Conjugate
Examples: In each of the following, express with a rational denominator.
[more examples next slide]

14. More examples

15. Exercise: Express the following fraction with a rational denominator.
Harder Type questions.
Express the following as a single fraction with a rational denominator.
Example
A possible method to solve this problems is to RATIONALISE the denominators
of each fraction first, then combine the results.

16. Exercise: Express the following as a single fraction with a rational denominator.