Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our User Agreement and Privacy Policy.

Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our Privacy Policy and User Agreement for details.

Like this presentation? Why not share!

886 views

Published on

Radical Notation for nth Roots

No Downloads

Total views

886

On SlideShare

0

From Embeds

0

Number of Embeds

96

Shares

0

Downloads

17

Comments

0

Likes

1

No embeds

No notes for slide

- 1. SECTION 8-4 Radical Notation for nth Roots
- 2. WARM-UP What is the length of the side of a cube whose volume is 512 cm3?
- 3. WARM-UP What is the length of the side of a cube whose volume is 512 cm3?
- 4. WARM-UP What is the length of the side of a cube whose volume is 512 cm3? V = 512
- 5. WARM-UP What is the length of the side of a cube whose volume is 512 cm3? V = 512 3 V=s
- 6. WARM-UP What is the length of the side of a cube whose volume is 512 cm3? V = 512 3 V=s 3 s = 512
- 7. WARM-UP What is the length of the side of a cube whose volume is 512 cm3? V = 512 3 V=s 3 s = 512 1 1 3 (s ) = 5123 3
- 8. WARM-UP What is the length of the side of a cube whose volume is 512 cm3? V = 512 3 V=s 3 s = 512 1 1 3 (s ) = 5123 3 s = 8 cm
- 9. WARM-UP What is the length of the side of a cube whose volume is 512 cm3? V = 512 8 cm 3 V=s 8 cm 8 cm 3 s = 512 1 1 3 (s ) = 5123 3 s = 8 cm
- 10. n th ROOTS 1 x is the nth root of x n
- 11. n th ROOTS 1 x is the nth root of x n Square root of x:
- 12. n th ROOTS 1 x is the nth root of x n 1 x Square root of x: 2
- 13. n th ROOTS 1 x is the nth root of x n 1 x= x Square root of x: 2
- 14. n th ROOTS 1 x is the nth root of x n 1 x= x Square root of x: 2 Cube root of x:
- 15. n th ROOTS 1 x is the nth root of x n 1 x= x Square root of x: 2 1 x Cube root of x: 3
- 16. n th ROOTS 1 x is the nth root of x n 1 x= x Square root of x: 2 1 3 x= x Cube root of x: 3
- 17. n th ROOTS 1 x is the nth root of x n 1 x= x Square root of x: 2 1 3 x= x Cube root of x: 3 nth root of x:
- 18. n th ROOTS 1 x is the nth root of x n 1 x= x Square root of x: 2 1 3 x= x Cube root of x: 3 1 x nth root of x: n
- 19. n th ROOTS 1 x is the nth root of x n 1 x= x Square root of x: 2 1 3 x= x Cube root of x: 3 1 n x= x nth root of x: n
- 20. n th ROOTS 1 x is the nth root of x n 1 x= x Square root of x: 2 1 3 x= x Cube root of x: 3 1 n x= x nth root of x: n ***Notice: In radical notation, if there is no number in the “seat,” it is understood to be a square root
- 21. DEFINITION For any nonnegative real number x and any integer n ≥ 2, 1 n x=x n
- 22. DEFINITION For any nonnegative real number x and any integer n ≥ 2, 1 n x=x n (the nth root of x)
- 23. EXAMPLE 1 Evaluate without using a calculator. 3 6 a. 27 b. 64
- 24. EXAMPLE 1 Evaluate without using a calculator. 3 6 a. 27 b. 64 =3
- 25. EXAMPLE 1 Evaluate without using a calculator. 3 6 a. 27 b. 64 =3 =2
- 26. EXAMPLE 2 Use a calculator to estimate to the nearest hundredth. 5 4 a. 15 b. 4829 c. 2401
- 27. EXAMPLE 2 Use a calculator to estimate to the nearest hundredth. 5 4 a. 15 b. 4829 c. 2401 ≈ 3.87
- 28. EXAMPLE 2 Use a calculator to estimate to the nearest hundredth. 5 4 a. 15 b. 4829 c. 2401 ≈ 3.87
- 29. EXAMPLE 2 Use a calculator to estimate to the nearest hundredth. 5 4 a. 15 b. 4829 c. 2401 ≈ 3.87
- 30. EXAMPLE 2 Use a calculator to estimate to the nearest hundredth. 5 4 a. 15 b. 4829 c. 2401 ≈ 3.87 ≈ 5.45
- 31. EXAMPLE 2 Use a calculator to estimate to the nearest hundredth. 5 4 a. 15 b. 4829 c. 2401 ≈ 3.87 =7 ≈ 5.45
- 32. NOTICE 1 1 1 5 4 15 = 15 ; 4829 = 4829 ; 2401 = 2401 2 5 4
- 33. ROOT OF A POWER THEOREM For all positive integers m > 1 and n ≥ 2, and all nonnegative real numbers x, m ( x) m n m n x= =x n
- 34. EXAMPLE 3 Simplify, for x ≥ 0. 3 4 8 18 a. x b. x
- 35. EXAMPLE 3 Simplify, for x ≥ 0. 3 4 8 18 a. x b. x 1 8 = (x ) 4
- 36. EXAMPLE 3 Simplify, for x ≥ 0. 3 4 8 18 a. x b. x 1 8 = (x ) 4 2 =x
- 37. EXAMPLE 3 Simplify, for x ≥ 0. 3 4 8 18 a. x b. x 1 1 8 18 = (x ) = (x ) 3 4 2 =x
- 38. EXAMPLE 3 Simplify, for x ≥ 0. 3 4 8 18 a. x b. x 1 1 8 18 = (x ) = (x ) 3 4 2 6 =x =x
- 39. EXAMPLE 4 Suppose x ≥ 0. Rewrite using rational exponents. 6 34 a. x 2 b. x
- 40. EXAMPLE 4 Suppose x ≥ 0. Rewrite using rational exponents. 6 34 a. x 2 b. x 1 1 = (x ) 2 6
- 41. EXAMPLE 4 Suppose x ≥ 0. Rewrite using rational exponents. 6 34 a. x 2 b. x 1 1 = (x ) 2 6 1 =x 12
- 42. EXAMPLE 4 Suppose x ≥ 0. Rewrite using rational exponents. 6 34 a. x 2 b. x 1 1 1 1 2 = (x ) = ((x ) ) 3 2 6 4 1 =x 12
- 43. EXAMPLE 4 Suppose x ≥ 0. Rewrite using rational exponents. 6 34 a. x 2 b. x 1 1 1 1 2 = (x ) = ((x ) ) 3 2 6 4 1 1 1 = (x ) =x 3 2 12
- 44. EXAMPLE 4 Suppose x ≥ 0. Rewrite using rational exponents. 6 34 a. x 2 b. x 1 1 1 1 2 = (x ) = ((x ) ) 3 2 6 4 1 1 1 = (x ) =x 3 2 12 1 =x 6
- 45. EXAMPLE 5 Rewrite using radical signs. 1 4 a. x b. x 3 7
- 46. EXAMPLE 5 Rewrite using radical signs. 1 4 a. x b. x 3 7 3 =x
- 47. EXAMPLE 5 Rewrite using radical signs. 1 4 a. x b. x 3 7 3 7 4 =x =x
- 48. EXAMPLE 5 Rewrite using radical signs. 1 4 a. x b. x 3 7 3 7 4 =x =x or
- 49. EXAMPLE 5 Rewrite using radical signs. 1 4 a. x b. x 3 7 3 7 4 =x =x or 4 ( x) 7 =
- 50. HOMEWORK p. 497 #1-29 “The only way most people recognize their limits is by trespassing on them.” - Tom Morris

No public clipboards found for this slide

×
### Save the most important slides with Clipping

Clipping is a handy way to collect and organize the most important slides from a presentation. You can keep your great finds in clipboards organized around topics.

Be the first to comment