Operations with Surds AS Maths

Which is the odd one out?

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.

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?

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

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!

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)

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)

Have a go... Example 6 Example 7

Solutions Example 6 a b c d

Solutions Example 7 a b c d e f

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!

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

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!

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

Subtracting Surds Example 9

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.

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

(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…

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

Examples Simplify in lowest terms. You must rationalize the denominator. 23. 24.

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