1 / 12

ALGEBRA – LESSON 108

This lesson focuses on understanding square roots and solving radical equations effectively. It outlines essential steps, including isolating the radical, squaring both sides, solving the equation, and checking the solution for accuracy. Practice problems with detailed solutions are provided to reinforce concepts. This lesson is designed for students preparing for exams or seeking to enhance their algebra skills. Homework assignments are included to assess understanding and readiness for grading.

luigi
Télécharger la présentation

ALGEBRA – LESSON 108

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. ALGEBRA – LESSON 108 Square Roots, Radical Equations Be ready to grade the homework!

  2. Grade Scale – 30 possible 29.5 – 98% 22.5 – 75% 29 – 97% 22 – 73% 28.5 – 95% 21.5 – 72% 28 – 93% 21 – 70% 27.5 – 92% 20.5 – 68% 27 – 90% 20 – 67% 26.5 – 88% 19.5 – 65% 26 – 87% 19 – 63% 25.5 – 85% 18.5 – 62% 25 – 83% 18 – 60% 24.5 – 82% 17.5 – 58% 24 – 80% 17 – 57% 23.5 – 78% 16.5 – 55% 23 – 77% 16 – 53%

  3. Square Roots Whenever we want to “get rid” of a radical sign, we will square the radical. 4 Steps to remember: 1. Isolate the radical 2. Square both sides 3. Solve 4. Check

  4. Square Roots – Just watch Solve: Öx – 2 – 6 = 0 Öx – 2 = 6 (Öx – 2)2 = 62 x – 2 = 36 x = 38 Check: Ö38 – 2 – 6 = 0 Ö36 – 6 = 0 6 – 6 = 0 x = 38

  5. Square Roots – Just watch Solve: Öx2 + 9 – 5 = 0 Öx2 + 9 = 5 Ö42 + 9 = 5 (Öx2 + 9)2 = 52 Ö25 = 5 x = 4 x2 + 9 = 25 x2 = 16 Ö(-4)2 + 9 = 5 x2 – 16 = 0 (x + 4)(x – 4)= 0 Ö25 = 5 x = -4 x = -4 or 4

  6. Square Roots Solve: Öx – 7 + 3 = -4 Öx – 7 = -7 (Öx – 7)2 = (-7)2 x – 7 = 49 x = 56 Check: Ö56 – 7 + 3 = -4 Ö49 + 3 = -4 7 + 3 = -4 #1 Empty set

  7. Square Roots Solve: Öx – 6 + 8 = 2 Öx – 6 = -6 (Öx – 6)2 = (-6)2 x – 6 = 36 x = 42 Check: Ö42 – 6 + 8 = 2 Ö36 + 8 = 2 6 + 8 = 2 #2 Empty set

  8. Square Roots Solve: Öe + 25 + 5 = e Ö0 + 25 + 5 = 0 Öe + 25 = e - 5 Ö25 + 5 = 0 (Öe + 25)2= (e - 5)2 Not a solution e + 25 = e2 – 10e + 25 Ö11 + 25 + 5 = 11 Ö36 + 5 = 11 0 = e2 – 11e e = 11 0 = e(e – 11) e = 0 or 11 #3

  9. Square Roots Solve: Ö x – 1 – 3 + x = 0 Ö5 – 1 – 3 + 5 = 0 Ö x – 1 = 3 – x Ö4 + 2 = 0 (Ö x – 1)2= (3 – x)2 Not a solution x – 1 = 9 – 6x + x2 Ö2 – 1 – 3 + 2 = 0 Ö1 – 1 = 0 0 = x2 – 7x + 10 x = 2 0 = (x – 5)(x – 2) x = 5 or 2 #4

  10. Square Roots Solve: Ö2x – 3 = Öx + 2 Ö2(5) – 3 = Ö5 + 2 Ö7 = Ö7 (Ö2x – 3)2= (Öx + 2)2 x = 5 2x – 3 = x + 2 x – 5 = 0 x = 5 #5

  11. Homework: Worksheet

  12. Square Roots Solve: 2Öx + 3x - 1 = 0 2 + 3 - 1 = 0 2Öx = -3x + 1 (2Öx )2= (-3x + 1)2 Not a solution 4x = 9x2 – 6x + 1 2(1/3) + 3(1/9) – 1 = 0 2/3 + 1/3 – 1 = 0 0 = 9x2 – 10x + 1 x = 1/9 Use Quadratic Formula x = 1 or 1/9 #4

More Related