1 / 10

Math 025 Section 10.3 Radicals

Math 025 Section 10.3 Radicals. Properties of multiplication and division of radicals. Ö a. ·. Ö b. =. Ö ab. Ö a. ·. Ö a. =. Ö a 2. =. a. Ö a. Ö. a b. =. Ö b. Simplify the following:. Ö 2x 2. Ö 32x 5. =. Ö 64x 7. =. Ö 64x 6 Ö x. = 8x 3 Ö x. Ö 5( Ö 2 – Ö 3 ). =.

aneko
Download Presentation

Math 025 Section 10.3 Radicals

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. Math 025 Section 10.3Radicals

  2. Properties of multiplication and division of radicals Öa · Öb = Öab Öa · Öa = Öa2 = a Öa Ö a b = Öb

  3. Simplify the following: Ö2x2 Ö32x5 = Ö64x7 = Ö64x6Öx = 8x3Öx Ö5(Ö2 – Ö3 ) = Ö10 – Ö15 (Ö2 – 3x)(Ö2 + x) = 2 + xÖ2 – 3xÖ2 – 3x2 = 2 – 2xÖ2 – 3x2

  4. Simplify the following: (Ö5 – 3)(Ö5 + 1) = 5 + Ö5 – 3Ö5 – 3 = 2 – 2Ö5 (Öx – 5)2 (Öx – 5)(Öx – 5) = = x – 5Öx – 5Öx + 25 = x – 10Öx + 25

  5. (Ö5 – 3)(Ö5 + 3) = 5 + 3Ö5 – 3Ö5 – 9 = 5 – 9 = -4 In the preceding example ( Ö5 – 3) and ( Ö5 + 3) are conjugates of each other. Whenever we multiply conjugates, (a – b)(a + b) = a2 – b2 so (x – 3)(x + 3) = x2 – 9 (Öx – 2)(Öx + 2) = x – 4 (Ö5 – Ö8)(Ö5 + Ö8) = 5 – 8 = -3

  6. Simplify the following: (Ö8 – 3)(Ö8 + 3) = 8 – 9 = -1 (Öx + 5) (Öx – 5) = x – 25 = 12 – 17 (Ö12 – Ö17) (Ö12 + Ö17) = -5

  7. A radical expression is not considered to be in simplest form if a radical remains in the denominator. The procedure used to remove a radical from the denominator is called rationalizing the denominator. Simplify: 2 2 Ö3 2Ö3 = = · Ö3 Ö3 Ö3 3 4 4 Ö6 4Ö6 2Ö6 = = = · Ö6 Ö6 Ö6 6 3

  8. Simplify: Ö Ö27a 27a = = Ö9 = 3 Ö3a 3a Ö Ö Ö9xy2 9xy2 y2 = = Ö27x 27x 3 Öy2 y Ö3 yÖ3 = = = Ö3 Ö3 Ö3 3

  9. When the denominator contains a radical expression with two terms, simplify by multiplying the numerator and denominator by the conjugate of the original denominator. Simplify: Ö2y Ö2y (Öy – 3) Ö2y2 – 3Ö2y = · = Öy + 3 (Öy + 3) (Öy – 3) y – 9 yÖ2 – 3Ö2y = y – 9

  10. When the denominator contains a radical expression with two terms, simplify by multiplying the numerator and denominator by the conjugate of the original denominator. Simplify: Ö2 Ö2 (Ö2 – Ö6) 2 – Ö12 = = Ö2 + Ö6 (Ö2 + Ö6) (Ö2 – Ö6) 2 – 6 2 – 2Ö3 2(1 – Ö3 ) = = – -4 4 1 – Ö3 = – 2

More Related