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
Log in with your personal details OR click “Do this homework for fun” – copy questions, working & answers in your independent study book. DUE NEXT LESSON!

13. 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

14. 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!

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

16. Subtracting Surds Example 9

17. 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…
17.
Since there is a radical in the denominator (bottom) of the fraction, we must multiply by the conjugate in order to rationalise the denominator.

18. Definition of a conjugate
Given the surd
Conjugate looks like
Hint
The conjugate is the same as the original
Only the sign in between the expression changes

19. (get the radical out of the bottom)
Now, let’s look back at that last example & rationalize the denominator
So next we must multiply by the conjugate to rationalize the denominator!
(get the radical out of the bottom)
We were at this step…

20. Practice finding the conjugate
Given the expression
Find the conjugate
18.
19.
20.
21.
22.
23.

21. Examples
Simplify in lowest terms. You must rationalize the denominator.

22. Examples
Simplify in lowest terms. You must rationalize the denominator.
25.