Transcript Simplifying Surds

Simplifying Surds

Look at the example and try to
work out how to get to the
answer

Stuck? Use the hint cards to
help (try to only use one at a
time!)

When you have worked it out,
write the rule on your
worksheet:
Simplify:
108
‘When simplifying surds, always
look for a factor that is a ….’

Now try the green, amber and
red questions!
Answer:
6 3
HINT CARD 1
HINT CARD 2
HINT CARD 3
HINT CARD 1
Use the following rule:
ab  a  b  a  b
Simplifying Surds
HINT CARD 2
 Look
for a factor that is a square number
and write it as a sum e.g.
72  9  8  9  8
Simplifying Surds
HINT 3
 Follow
this worked example:
75  25  3
 25  3
Look for a factor
that is a square
number
 5 3
5 3
This is how the
final answer
should be written
Simplifying Surds
Squaring Surds
 Try
these sums on your
calculator
 What
do you find out?
 Write
the rule on your
sheet:
‘When we square a surd…’

Try the green, amber
and red sums.
1.
36  36 
2.
100  100 
3.
3 3 
4.
20  20 
5. 2136   2136 
Why Bother With Surds?

Type each of the sums into
the calculator.

Look carefully at the
answer and think about
why we use surds



Use the hint card if you
need help
Write your findings on your
sheet
Try the green, amber and
red questions
These are not surds:
25
225
196
64
81
144
These are surds:
7
24
2
92
12
HINT CARD
HINT
 Look
at the numbers after the decimal
point.
 What
words would you use to describe
the order that they appear?
Why bother with surds?
Adding Surds
how to
collect like terms in
algebra?
Example:
 Remember
 Adding
and subtracting
surds works in exactly
the same way!
 Look
at the worked
example and discuss
the question
2 34 3 
6 3
Your Turn:
8 5 2 34 5  3
HINT CARD
HINT 1
 Think
of each surd as ‘x’ and collect like
terms like you would in algebra! E.g.
4 2 2 3 2
Think of these as
4x – 2x =
Adding surds
Multiplying Surds

When multiplying surds, write
out the expression in full before
attempting to simplify it.

Sound familiar? It’s exactly the
same as algebra!

Can you fill in the ‘working out’
for this question? Use the hints
to help you.

Fill in the rule on your sheet:
‘When multiplying surds, always
write out…’
Try the green, amber and red
questions!
Simplify:
3 5 7 2 
Answer: 21 10
HINT CARD
HINT
 Write
out the sum in the longest way first…
2 7 4 6
 2 7  4 6
 8 7  6
 8 42
…then multiply out the
whole numbers…
…then multiply
the surds together!
Multiplying surds