1. Unit 6 : Operations with Radical Expressions
Goal:
Add, subtract, multiply and divide radical expressions.

2. Recall – when must you simplify a radical?
A radical is considered simplified when:
- 1) there are no perfect square factors in the radicand,
- 2) when there are no fractions in the radicand, and
- 3) no radicals appear in the denominator of a fraction.
This is MUST KNOW STUFF! Why – because you have to be able to DO IT. 2

3. Adding and Subtracting
You can use the distributive property to simplify sums and differences……

4. Adding and Subtracting
What about this one? 4

5. Your turn

6. Multiplying Radicals – you can multiply what is UNDER the radical sign together….6

7. Distributive Property and FOIL work too…. Simplify if necessary…..7

8. Patterns are helpful! Simplify if necessary…..8

9. Your turn 9

10. 12.2 – Vocabulary - Conjugates
The expressions above are called conjugates because their products do NOT produce radicals

11. Conjugate Examples – note pattern:
Expression Conjugate Product 11

12. Simplify the expression12

13. Simplify the expression – Your turn13

14. Check that is a solution of
Checking Solutions
Check that is a solution of
It IS a solution! 14

15. Checking Solutions - Your turn
Check that is a solution of
Yes it is. 15

16. You and a friend are spending the summer working on a boat
You and a friend are spending the summer working on a boat. The distance that you can see to the horizon can be modeled by the following equation, where h is your eye level height (in feet), above the water.
Suppose your eye level height is 20 feet and your friend’s is 28 feet. Write an expression that shows how much farther your friend can see than you. 16

17. Homework
P719, even