Download Surd Algebra - Hinchingbrooke

Lesson Objectives:
Revise Surd Algebra
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
ab  a  b
ab  a  b
a a
a
a

b
b
a a a
a b  a  b
1
a

a
a
 a
2
a
If you have finished check to see if you get the same results for
cube roots.
Four Main Rules of Surd Algebra:
1) You can collect like surds together
3 2 4 5  2 2 5  2 2 6 5
2) You can multiply two surds together
3 2  4 5  12 10
3) The square root of ‘a’ times the
square root of ‘a’ is always ‘a’
5  5  25  5
4) You can simplify a surd fraction by
rooting the tops and bottoms
separately
16
16 4


25
25 5
Compare this to:
3x + 4y – x +2y = 2x + 6y
Compare this to:
3x × 4y = 12xy
1) 4 3  5 3  2 7
2)
3)
8 34 3
12 6  2 6
4) 5 2  4 3  2 2
5)
6)
19) 6 6  3 5
10)
4 2 5
11)
5 32 2
20)
12)

21) 10 5  2 5
13)
4 3

2
2 3 5 3 3 3 7 3
22) 81
9
16
4
 3
14)
6 32 2 2 34 2
15)
3 2 2 8
16)
4 3 3 8
3
7) 6  4 3  3  4 3
 2
17) 6 12  2 2
9) 4 7  10 3  6 7  3
18) 2 15  9 2
2
8)
2 36
Simplify each
expression
If you do it
correctly they
should pair
up!
5 32 2
12 6  2 6
8 34 3
2 36
3 2 2 8

4 3

2
 3
3
2 3 5 3 3 3 7 3
5 2 4 32 2
6 32 2 2 34 2
10 5  2 5
16
4
 2
4 2 5
4 3 5 3 2 7
4 7  10 3  6 7  3
81
9
2
6  4 3 3 4 3
4 3 3 8
6 12  2 2
6 6 3 5
2 15  9 2
Can you complete this addition square?
Can you complete this multiplication square?
Make up your own one of each type!
Important Skills:
Simplifying a surd:
Rationalising a surd
Simplify these surds:
a)
18
b)
45
c)
32
d)
28
e)
27
f)
80
g)
300
h)
48
i)
63
j)
75
k)
50
l)
108
Simplify these expressions:
8  18
50  18  8
32  8
32  8
3  12
20 5  5 20
99  44  11
20  5
27  27
Rationalise:
4
2√3 - 4
Simplify:
4
2√3
+
5
4√7
Simplify:
(3 √5)2
(3 √5)3
(3 √5)4
Solve:
(3x + 4√5) = 2
(3x - 4√3)
Basic Surd Skills
1) Simplify/Cancel single surd terms
2) Add and subtract Surds
3) Multiply and divide surds
4) Rationalise Surds