1. Simplifying Radicals

2. Radicals

3. Simplifying Radicals Express 45 as a product using a square number
Separate the product
Take the square root of the perfect square

4. Some Common Examples

5. Harder Example
Find a perfect square number that divides evenly into by testing 4, 9, 16, 25, 49 (this works)

6. Addition and Subtraction
You can only add or subtract “like” radicals
You cannot add or subtract with

7. More Adding and Subtracting
You must simplify all radicals before you can add or subtract

8. Multiplication
Consider each radical as having two parts. The whole number out the front and the number under the radical sign.
You multiply the outside numbers together and you multiply the numbers under the radical signs together

9. More Examples
Note that can be simplified

10. Try These

11. Division
As with multiplication, we consider the two parts of the surd separately.

12. Division

13. Important Points to Note
Radicals can be separated when you have multiplication and division
However
Radicals cannot be separated when you have addition and subtraction

14. Rational Denominators
Radicals are irrational. A fraction with a radical in the denominator should to be changed so that the denominator is rational.
Here we are multiplying by 1
The denominator is now rational

15. More Rationalising Denominators
Multiply by 1 in the form
Simplify

16. Review Difference of Squares
When a radical is squared, it is no longer a radical. It becomes rational. We use this and the process above to rationalise the denominators in the following examples.

17. More Examples
Here we multiply by 5 – which is called the conjugate of 5 +
Simplify

18. Another Example
Here we multiply by the conjugate of which is
Simplify

19. Try this one
The conjugate of is
Simplify
See next slide

20. Continuing

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