1. Operations with Surds
AS Maths

2. Which is the odd one out?

3. What is a surd? GOALS: Know what is meant by surd form.
A surd is the result of taking the square root of a non-perfect square (there will still be a in your answer!)
Ex:
GOALS:
Know what is meant by surd form.
Understand the process of simplifying surds.
Know how to rationalise a surd.

4. Simplifying Surds Example 1
You can simplify some square roots into surds.
Rules for surds
Think of square numbers...do any of them go into 27?

5. Simplifying Surds Example 2
Try out this one
What square number goes into 75?

6. Simplifying Surds Example 3
Sometimes you may need more than one breakdown...
This can be broken down further because a perfect square goes into 8
TIP: Look for Prime Factors to get there faster!

7. Multiplying Surds Example 4
Rules for surds
When multiplying two separate radicals, we use the previous rule backwards & combine them under one radical.
(a)
(c)
In this case, simply
distribute then simplify!
(d)
(b)

8. Dividing Surds Example 5
Rules for surds
When dividing two separate radicals, we can combine them under one root or vice versa.
(a)
(c)
(b)

9. Have a go...
Example 6
Example 7

10. Solutions
Example 6
a b
c d

11. Solutions
Example 7
a b
c d
e f

12. Independent Study Mymaths.co.uk Username: bilborough Password: normal
Click on:
A Levels
Core 1
Indices & Surds
Surds Part 1
Online Homework
“Do this homework for fun” – copy questions, working & answers in your independent study book. DUE NEXT LESSON!

13. As you come in...
1st – Make a name tent 2nd – get out your independent study (mymaths Surds Part 1). Make sure your name, the title, and date are in the heading

14. Adding Surds Rules for surds
Think of adding radicals as combining like terms.
You can only combine radicals that match.
Note: The “like term” in this expression is
so we can combine it’s coefficients
Rules for surds

15. If the roots don’t match, see if you can simplify
Adding Surds Example 8
If the roots don’t match, see if you can simplify
first!

16. Subtracting Radicals Rules for surds
Just as we did on the previous slide, when subtracting radicals  combine like terms!
Rules for surds

17. Subtracting Surds Example 9

18. Expanding Brackets Example 10
Simplify. (Hint: multiply using F.O.I.L. or a grid)

19. Tarsia Time!
Using the skills from this lesson and last, complete the puzzle in groups.

20. Rule: Your final answer cannot contain a surd in the denominator!
Rationalising Surds
Rule: Your final answer cannot contain a surd in the denominator!
Let’s take a look at an example where we will be left with a radical in the denominator…
Example 11
Since there is a radical in the denominator (bottom) of the fraction, we must multiply by the conjugate in order to rationalise the denominator.

21. What’s a conjugate? Rules for surds Given the surd
Conjugate looks like
Hint
The conjugate is the same as the original
Only the sign in between the expression changes

22. (get the surd out of the bottom)
Now, let’s look back at that last example & rationalise the denominator Example 11 (Cont’d…)
We were at this step…
We must multiply the TOP and BOTTOM by the conjugate to rationalise the denominator!
(get the surd out of the bottom)

23. Rationalising Surds Example 12
Express in the form , where c and d are integers.
Solution:
Multiply the top & bottom by the conjugate!

24. Homework

25. TEST on surds – Tuesday, Sept 16th
Surds Homework
Homework should be done on loose paper.
Homework & answers are on moodle.
Write all questions, show all work, and mark your answers in a colourful pen. If you incur a wrong answer, show corrected work.
Due Tuesday, Sept 16th
TEST on surds – Tuesday, Sept 16th

26. Extra Resource Khan academy – great maths videos!