1 / 6

EXAMPLE 1

a. Because n = 3 is odd and a = –216 < 0, –216 has one real cube root. Because (–6) 3 = –216 , you can write = 3 √ –216 = –6 or (–216) 1/3 = –6.

shani
Download Presentation

EXAMPLE 1

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. a. Because n = 3 is odd and a = –216 < 0, –216 has one real cube root. Because (–6)3= –216, you can write = 3√–216 = –6 or (–216)1/3 = –6. b. Because n = 4 is even and a = 81 > 0, 81 has two real fourth roots. Because 34 = 81 and (–3)4 = 81, you can write ±4√ 81 =±3 EXAMPLE 1 Find nth roots Find the indicated real nth root(s) of a. a. n = 3, a = –216 b. n = 4, a = 81 SOLUTION

  2. 1 1 23 323/5 64 ( )3 = (161/2)3 = 43 = 43 = 64 = = 16  1 1 1 1 1 1 = = = = ( )3 (321/5)3 323/5 32  5 8 23 8 = = = = EXAMPLE 2 Evaluate expressions with rational exponents Evaluate (a) 163/2 and (b)32–3/5. SOLUTION Radical Form Rational Exponent Form a. 163/2 163/2 b. 32–3/5 32–3/5

  3. Keystrokes Expression Display 9 1 5 7 3 4 12 3 8 7  c. ( 4 )3 = 73/4 EXAMPLE 3 Approximate roots with a calculator a. 91/5 1.551845574 b. 123/8 2.539176951 4.303517071

  4. for Examples 1, 2 and 3 GUIDED PRACTICE Find the indicated real nth root(s) of a. 1. n = 4, a = 625 3. n = 3, a = –64. SOLUTION ±5 SOLUTION –4 2.n = 6, a = 64 4. n = 5, a = 243 SOLUTION ±2 SOLUTION 3

  5. 1 3 for Examples 1, 2 and 3 GUIDED PRACTICE Evaluate expressions without using a calculator. 5. 45/2 7. 813/4 27 SOLUTION 32 SOLUTION 6. 9–1/2 8. 17/8 SOLUTION SOLUTION 1

  6. Expression 10. 64 2/3 – 11. (4√ 16)5 12. (3√–30)2 for Examples 1, 2 and 3 GUIDED PRACTICE Evaluate the expression using a calculator. Round the result to two decimal places when appropriate. 9. 42/5 1.74 SOLUTION SOLUTION 0.06 SOLUTION 32 9.65 SOLUTION

More Related