1. Simplifying Radicals you solve them? Topic: Radical Expressions
Essential Question: How are radical expressions represented and how can
you solve them?
Simplifying Radicals

2. What numbers are perfect squares?
1 • 1 = 1
2 • 2 = 4
3 • 3 = 9
4 • 4 = 16
5 • 5 = 25
6 • 6 = 36
49, 64, 81, 100, 121, 144, ...

3. A List of Some Perfect Squares64
225 1 81
256 4
100
289 9
121 16
324
144 25
400
169 36
196 49
625

4. Simplify
= 2
= 4
That was easy!
= 5
= 10
= 12

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

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

7. 1. Simplify

8. Simplify .

9. Hint: In order to combine radicals they must be like terms
Combining Radicals +
To combine radicals: combine the coefficients of like radicals
Hint: In order to combine radicals they must be like terms

10. Simplify each expression

11. Simplify each expression: Simplify each radical first and then combine.

12. Simplify each expression: Simplify each radical first and then combine.

13. Simplify each expression

14. Simplify each expression

15. Hint: to multiply radicals they DO NOT need to be like terms
Multiplying Radicals *
To multiply radicals: multiply the coefficients and then multiply the radicands and then simplify the remaining radicals.
Hint: to multiply radicals they DO NOT need to be like terms

16. Multiply and then simplify

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

19. That was easy!

20. There is a radical in the denominator!
Simplify
Uh oh…
There is a radical in the denominator!
Whew! It simplified!

21. Simplify Uh oh… Another radical in the denominator!
Whew! It simplified again! I hope they all are like this!

22. 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.

23. Simplify Since the fraction doesn’t reduce, split the radical up.
Uh oh…
There is a fraction in the radical!
Simplify
Since the fraction doesn’t reduce, split the radical up.
How do I get rid of the radical in the denominator?
Multiply by the “fancy one” to make the denominator a perfect square!

24. 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.

25. 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.

26. Simplify
= X
= Y3
= P2X3Y
= 2X2Y
= 5C4D5

27. Simplify = = = =

28. Simplify .

29. Since there are no like terms, you can not combine.
Challenge:
Since there are no like terms, you can not combine.

30. How do you know when a radical problem is done?
No radicals can be simplified. Example:
There are no fractions in the radical. Example:
There are no radicals in the denominator. Example: