1. Simplifying Radicals

2. Perfect Squares 64
225 1 81
256 4
100
289 9
121 16
324
144 25
400
169 36
196 49

3. Simplify
= 2
= 4
= 5
This is a piece of cake!
= 10
= 12

4. Simplify Using Perfect Square Method
Find a perfect square that goes into 147

5. Find a perfect square that goes into 605
Simplify
Find a perfect square that goes into 605

6. Simplify = = = = = = = = = = Perfect Square Factor * Other Factor
LEAVE IN RADICAL FORM = = = = = =

7. Simplifying Radicals by Tree Method.
Simplify the following. Step one, break the number down into a factor tree. Step two: Circle any pairs. The pairs bust out of the klink. 2 10 5 2

8. So… which is really just… so it ends up like this…
This guy didn’t have a partner and so is left in prison
This guy gets away
This guy gets caught and is never heard from again
But teacher, teacher, what happens to the other guy?
He’s Dead, gone, went bye bye, won’t see him again!
The guy that got away
The guy left in prison

9. Another Example Simplify the following: Step 1: Make a factor tree
So that leaves:
Which is: 14 10 2 7 2 5

10. Cake Method
Video on Cake Method

11. Your Turn!
Simplify the following: 8

12. Simplify = =
LEAVE IN RADICAL FORM = = =

13. Simplify = =
LEAVE IN RADICAL FORM = = =

14. Adding or Subtracting Radicals
To add or subtract square roots you must have like radicands (the number under the radical). Then you add or subtract the coefficients!
Sometimes you must simplify first:

15. Example 1:

16. Try These

17. DO NOW

18. Multiplying Radicals *
To multiply radicals: multiply the coefficients and then multiply the radicands and then simplify the remaining radicals.

19. Radical Product Property
ONLY when a≥0 and b≥0
For Example:
Equal

21. Multiplying Radicals 1. Multiply terms outside the radical together.
2. Multiply terms inside the radical together.
3. Simplify.

22. Multiplication and Radicals
Simplify the expression:

23. Multiply then simplify

24. You can multiply using distributive property and FOIL.
Multiplying Radicals
You can multiply using distributive property and FOIL.

25. Multiply: You try.

26. Using the Conjugate to Simplify
Expression
Conjugate
Product
The radical “goes away” every time

27. _______ _______
To divide radicals: divide the coefficients, divide the radicands if possible, and rationalize the denominator so that no radical remains in the denominator

28. Radical Quotient Property
ONLY when a≥0 and b≥0
For Example:
Equal

29. That was easy!

30. Fractions and Radicals
Simplify the expressions:
There is nothing to simplify because the square root is simplified and every term in the fraction can not be divided by 10.
Make sure to simplify the fraction.

31. Dividing to Simplify Radicals
No radicals in the denominator allowed
Denominators must be “rationalized.”
Multiply by 1in the form of √ √ 3 1

32. Using the Conjugate to Simplify
Expression
Conjugate
Product
The radical “goes away” every time

33. Dividing to Simplify Radicals
conjugate
Multiply by 1in the form of
conjugate 5 1 11

34. Simplify: You try.

35. 42 cannot be simplified, so we are finished.
This cannot be divided which leaves the radical in the denominator. We do not leave radicals in the denominator. So we need to rationalize by multiplying the fraction by something so we can eliminate the radical in the denominator.
42 cannot be simplified, so we are finished.

36. This can be divided which leaves the radical in the denominator
This can be divided which leaves the radical in the denominator. We do not leave radicals in the denominator. So we need to rationalize by multiplying the fraction by something so we can eliminate the radical in the denominator.

37. This cannot be divided which leaves the radical in the denominator
This cannot be divided which leaves the radical in the denominator. We do not leave radicals in the denominator. So we need to rationalize by multiplying the fraction by something so we can eliminate the radical in the denominator.
Reduce the fraction.

38. Summary: COMBINE LIKE TERMS “Outside” NUMBERS x NUMBERS
To ADD and SUBTRACT
COMBINE LIKE TERMS
To MULTIPLY
“Outside” NUMBERS x NUMBERS
“Inside” NUMBERS x NUMBERS
DISTRIBUTE and FOIL
To DIVIDE
“Rationalize” denominator using 1
Use conjugate
ALWAYS SIMPLIFY AT THE END IF YOU CAN