1. Simplifying Radicals
Algebra

2. Radical Expressions – An expression that contains a square root
Radicand – The expression under the square root sign
Vocabulary

3. Properties

4. Use the prime factorization to break down the radicand
Every pair of numbers that are the same can be removed and be one number on the outside
Simplifying Radicals

5. Example

6. Variables can also be removed from under a radical sign
Remove matching pairs (even number exponents) and express as half as many outside the radical sign
Any result that has a odd exponent for a variable should be expressed as an absolute value
Simplifying Radicals

7. Illustration Consider the following analogy
Square root is a function. A lawn mower is a function.
Illustration

8. Illustration Lawnmower Input is long grass Output is grass pieces
Square Root
Input is everything under the radical sign
Output is everything outside the radical sign
Illustration

9. Illustration Lawnmower Grass that goes through the function is smaller
Square Root
Numbers and variables that come through the function are smaller
Illustration

10. Illustration Lawnmower
Grass that does not go through the function, is left attached to the roots, typically this is shorter, never longer
Square Root
Numbers and variables that do not go through the function, are left inside the radical, and are typically smaller
Illustration

11. Illustration Lawnmower
If you run over short grass, it does not go through the function, and is unchanged
Square Root
Numbers and variables that cannot be reduced, do not go through the function and are unchanged
Illustration

12. Example

13. When multiplying (dividing), the product (quotient) may allow further simplifying than the individual terms
Simplifying Radicals

14. Example

15. Example

16. Example

17. Example

18. Practice

19. Rationalizing a Denominator – A simplified radical does not include any radical signs in the denominator. To remove denominator radicals, multiply the numerator and the denominator by the radical in the denominator
Simplifying Radicals

20. Example

21. Example

22. Summary

23. Simplify each radical expression
Review Problems

24. Simplify each radical expression
Review Problems

25. Simplify each radical expression
Review Problems

26. Simplify each radical expression
Review Problems

27. Simplify each radical expression
Review Problems

28. Simplify each radical expression
Review Problems

29. Simplify each radical expression
Review Problems

30. Simplify each radical expression
Review Problems

31. Simplify each radical expression
Review Problems

32. Simplify each radical expression
Review Problems

33. Simplify each radical expression
Review Problems

34. Pages 582 – 583
57 – 71 all, 76, 83
Homework