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
625

3. Simplify
= 2
= 4
= 5
= 10
= 12

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

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

6. + To combine radicals: combine the coefficients of like radicals
Combining Radicals +
To combine radicals: combine the coefficients of like radicals

7. Simplify each expression

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

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

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

11. Simplify each expression

12. Simplify each expression

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

14. Multiply and then simplify

16. 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

17. That was easy!

18. 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.

19. 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.

20. 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.

21. Simplify
= X
= Y3
= P2X3Y
= 2X2Y
= 5C4D10

22. Simplify = = = =

23. = = ? = =