1. ‘When simplifying surds, always look for a factor that is a ….’
Answer:
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:
‘When simplifying surds, always look for a factor that is a ….’
Now try the green, amber and red questions!

2. HINT CARD 1

3. HINT CARD 2

4. HINT CARD 3

5. HINT CARD 1
Use the following rule:
Simplifying Surds

6. HINT CARD 2
Look for a factor that is a square number and write it as a sum e.g.
Simplifying Surds

7. HINT 3 Follow this worked example:
Look for a factor that is a square number
This is how the final answer should be written
Simplifying Surds

8. ‘When we square a surd…’
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. 2. 3. 4. 5.

9. Why Bother With Surds? These are not surds: These are 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:
These are surds:

10. HINT CARD

11. 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?

12. Adding Surds Example: Remember how to collect like terms in algebra?
Your Turn:
Remember how to collect like terms in algebra?
Adding and subtracting surds works in exactly the same way!
Look at the worked example and discuss the question

13. HINT CARD

14. HINT 1
Think of each surd as ‘x’ and collect like terms like you would in algebra! E.g.
Think of these as
4x – 2x =
Adding surds

15. ‘When multiplying surds, always write out…’
Simplify:
Answer:
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!

16. HINT CARD

17. HINT Write out the sum in the longest way first…
…then multiply out the
whole numbers…
…then multiply
the surds together!
Multiplying surds