6 1 properties of square roots

1. 6.1 Properties of Square Roots

2. Square Root Vocab The square root symbol is called a “ radical sign ” The number inside is the “ radicand ”

3. Properties: Product Property Quotient Property

4. Simplifying Square Roots A square root is simplified when the radicand has no perfect square factors (other than 1).

5. Method 1: Use Product Property to rewrite using largest perfect square factor. Simplify Example:

6. Method 2: Make a factor tree. Any number that “finds a date” gets to go outside the radical. Example:

7. Examples: Simplify:

8. You Try! Simplify:

9. More Examples: Simplify:

10. You Try! Simplify:

11. Using the Quotient Property Simplify

12. Examples: Simplify:

13. You Try! Simplify:

14. Evaluating Square Roots Plug in given values for each variable. USE PARENTHESES!! Simplify under the radical sign. Reduce/simplify the square root.

15. Example Evaluate when a = 2, b = -8, and c = 4.

16. Example Evaluate when a = 20 and b = 16

17. You Try! Evaluate when a = 2, b = -6, and c = -5.

18. Simplifying Radical Expressions Simplify the radical (square root) first. Then divide/reduce. Example:

19. Example: Simplify:

20. Example: Simplify:

21. Example: Simplify:

22. You Try!

23. Simplifying Variable Expressions For expressions like this: Simplify the number part as usual. Pairs of each variable go outside.

24. Example: Simplify

25. Example: Simplify

26. Example: Simplify

27. You Try! Simplify:

28. Example: Simplify

29. Example: Simplify

30. You Try! Simplify