1. 9.1 Radicals and Quadratic Equations By: Brian Levy Honors Geometry Period 9

2. Contents Objective: Simplify radical expressions and solve quadratic equations 1.Notes on Radicals 2.Practice with solving radical expressions 3.Practice with solving quadratic equations

3. Notes and Terms When a number is squared it is simply multiplied by itself –Ex. To find the square of 9 ….. 9X9 = 81 To find the inverse of squaring a number, you need to find its square root –? So, what’s a square root?

4. Notes and Terms A square root of a number is one of the two equal factors of that number –The square root of a positive number will be –1. Positive (+) –2. Negative (-) –Ex. Square root of 64 is 8…..8X8=64 –Ex. Square root of 64 is -8….(-8)X(-8)=64

5. Notes and Terms This is a radical sign –It indicates that you are supposed to find the square root of a number in terms of positive value. This is a radicand –It is the number or expression under the radical sign.

6. Notes and Terms Radical Expression is any expression having a term containing a radical sign Square root radicals are in simplest form when: –View Structure diagram on next slide

7. Notes and Terms Square root radicals In simplest form No fraction appears As a radical No integral radicand Has a square factor Other than 1 No radical is in the denominator

8. Notes and Terms Properties of Radicals (if x > 0 and y > 0) –1. –2. –3.

9. Notes and Terms If you ever can’t find the square root of a number, remember this helpful table Numbers on left Squares on right This is continuous 11 24 39 416 525 636 749 864 981 10100 11121 12144 13169 14196 15225 16256 17289 18324 19361 20400 21441 22484 23529 24576 25625

10. Let’s Practice Sample 1:

11. Let’s Practice S2 S3

12. Let’s Practice S4 S5-Simply square the number outside the radical sign. Then, times it by the radicand, without squaring he radicand.

13. Let’s Practice S6-Remember your brackets! Here’s an example –x² = 28

14. Let’s Practice S7We can solve this equation by using a simple form of the quadratic formula z² - 5z = 6 z² - 5z – 6 =0It is crucial to set your equation = to 0 and to remember brackets to group your final solution (z+1) (z-6) =0 z = -1 or z = 6 {-1,6}

15. Exercises for Practice Ex.1-SimplifyEx.2-Simplify Ex.3-SimplifyEx.4-Solve 9x² = 64

16. Exercises for Practice (Additional) The best all-around review for section 9.1 is in your 9.1 yellow radicals packet. On page 7, you will find 30 problems consisting of radical expressions, square roots, and quadratic equations. On page 8, you can check your work with the answers Mr. Pricci has provided.

17. Answers Samples

18. Answers Exercises

19. Works Cited Brown, Richard G., et al. Algebra: Structure and Method Book 1. Boston: Houghton Mifflin Company, 1997. Pricci, Vincent. “Radicals Notes.” Clarks Summit. 2008. Rhoad, Richard, et al. Geometry for Enjoyment and Challenge. Boston: McDougal Littell & Company, 1991.