SO x is a cubed root of t
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1 7.6nth Roots 1) What do we know about x because of the following equation x 3 = t? All in one.docx SO x is a cubed root of t 2) Definition of nth root: 3) Study example 1 4) Now try the following problem in your notes: b 3 = x so b is the 3rd root of x a. Explain how you could use the graph of y = x 8 to estimate the real 8 th root of 3. b. Estimate the real 8 th roots of 3. 8th roots of 3 include and (1.1472) 8 = 3... x 8 = y means x is an 8th root of y To estimate the 8th root of 3 write the equation x 8 = 3 (so x is the 8th root of 3) then graph each side and find the intersection. Jan 6 3:58 PM 1
2 5) Study example 2 6) (1/n) Exponent Theorem: 7) When working with the above theorem it is important to remember what about each of the following expressions: a. x x is nonnegative b. n n is an integer greater than 1 c. is the nth root of x Jan 6 3:59 PM 2
3 AdvancedAlgebra7.6nthRoots.notebook 8) Number of Real Roots Theorem: 9) Study example 3 10) Now try the following problem in your notes: a. Evaluate b. Evaluate c. Evaluate d. Evaluate OR OR Jan 6 4:02 PM 3
4 AdvancedAlgebra7.6nthRoots.notebook 11) Study example 4 12) Now try the following problem in your notes: a. Find all real solutions of x3 = 343 x is the cube root of 343 x= Jan 6 4:05 PM 4
5 13) Study example 5 14) Now try the following problem in your notes: a. Show that 1 i is a fourth root of 4. b. The number 4 has three more fourth roots. Guess what they are. Check your guesses by multiplication. Jan 6 4:05 PM 5
6 15) Now try the following problem in your notes: a. Between which two consecutive integers is the real solution to x 5 = 500? Do not use a calculator. x is the 5 th root of 500 Some number times itself five time equals 500 x = Between 3 and 4 Jan 6 4:06 PM 6
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21 Notes 7 6: N th Roots b n = x Dec 22 8:25 AM 21
22 x 1/n square (second) root cube (third) root fourth root Dec 22 8:28 AM 22
23 Simplify: ⅓ = ¼ = ½ = Solving equations using n th roots. 1. x ½ = x ⅓ 3 = 9 Dec 22 8:36 AM 23
24 3. 8x 6 = x 3 = x 1/3 5 = x 1/2 = 36 Dec 22 8:37 AM 24
25 How many real roots does a real number have? The number of real n th roots of a real number k is the number of points of intersection of the line y = k with the power function. y = x n How many real 5 th roots does 2 have? Look for intersection of y = and y = x. How many real square roots does 5 have? Look for intersection of y = and y = x. Dec 22 8:43 AM 25
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27 2 real n th roots 1 real n th root 0 real n th roots 1 real n th root Feb 4 6:55 AM 27
28 Show that 1 i is a 4th root of 4 The number 4 has 3 more 4th roots. Guess what they are. Sep 19 9:15 AM 28
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50 Attachments All in one.docx
AdvAlg9.7LogarithmsToBasesOtherThan10.notebook. March 08, 2018
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GAMINGRE 8/1/ of 7
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