1. Lesson Objectives:
Revise Surd Algebra

2. Here are some statements about surds.
Decide if they are: True for any numbers a and b
True for some numbers a and b
Never true
If you have finished check to see if you get the same results for cube roots.

3. Four Main Rules of Surd Algebra:
You can collect like surds together
You can multiply two surds together
The square root of ‘a’ times the square root of ‘a’ is always ‘a’
You can simplify a surd fraction by rooting the tops and bottoms separately
Compare this to:
3x + 4y – x +2y = 2x + 6y
Compare this to:
3x × 4y = 12xy

4. Simplify each expression If you do it correctly they should pair up!1)
10)
19) 2)
11)
20)
21) 3)
12)
22) 4)
13) 5)
14) 6)
15)
Simplify each expression
If you do it correctly they should pair up! 7)
16) 8)
17) 9)
18)

6. Can you complete this addition square?
Can you complete this multiplication square?
Make up your own one of each type!

7. Important Skills:
Simplifying a surd:
Rationalising a surd

8. Simplify these surds:
a) b) c)
d) e) f)
g) h) i)
j) k) l)
Simplify these expressions:

9. Rationalise:
2√3 - 4

10. Simplify:
2√ √7

11. Simplify: (3 √5)2
(3 √5)3
(3 √5)4

12. Solve: (3x + 4√5) = 2
(3x - 4√3)

13. Basic Surd Skills
Simplify/Cancel single surd terms
Add and subtract Surds
Multiply and divide surds
Rationalise Surds