24
Advanced Algebra / Trigonometry Section 7-4 nth Roots
| Date post: | 01-Jan-2016 |
| Category: |
Documents |
| Upload: | otto-kline |
| View: | 38 times |
| Download: | 5 times |
Advanced Algebra / Trigonometry
Section 7-4nth Roots
Target Goals
1) Simplify Radicals2) Use a Calculator to Approximate
Radicals
Please select a Team.
A. B. C. D. E. F. G. H. I. J.
0 0 0 0 000000
A. Team 1B. Team 2C. Team 3D. Team 4E. Team 5F. Team 6G. Team 7H. Team 8I. Team 9J. Team 10
Response Grid
Countdown
10
Simplifying Radicals (finding roots)nth
Vocab
Review
Square Root:
The root that you've already worked with is the 2nd root.nth
:Ex 49 7
2For any real numbers and , if , then is the square root of .a b a b a b
The 2nd root is usually called the "square root" and is denoted with the symbol, .
7 is the principal (positive) square root of 49.
49 7 7 is the opposite of the principal square root of 49.
49 7 7 represent both square roots of 49.
Simplifying Radicals (finding roots)nthNew
5th roots, etc.
** An even root of a positive number will have a positive and negative answer.
Now we will be working with 3rd roots "cube roots", 4th roots,
Vocab
Unless indicated, we will only write the positive (principal) root.
** An odd root of a positive number will have a positive answer.
4 256 4:Ex
The th root is denoted with the symbo l .nn
5 32 2 3 27 3
** An even root of a negative number is a non-real solution (will talk about later).
** An odd root of a negative number will have a negative answer.
4 16 2
Perfect Squares21 11 1
22 44 2 23 99 3
2 6 44 16 1 2 5 55 25 2 2 6 66 36 3 2 9 77 49 4 2 4 88 64 6 2 1 99 81 8
210 10 10 100 0 211 12 11 121 1 212 14 14 144 2 213 16 19 169 3 214 19 16 196 4 215 22 15 225 5
22 2 xx x x
22 4 4 2x x x x
23 6 6 3x x x x
Divide exponent by 2.
Perfect Cubes33 11 1 1 33 3 3 xx x x
Divide exponent by 3.
33 22 8 8 33 33 27 27 33 44 64 64 335 125 125 5 336 216 216 6 337 343 343 7 338 512 512 8 339 729 729 9
3 310 1000 1000 10
32 6 3 6 2x xx x
33 9 3 9 3x xx x
Perfect Quads44 11 1 1 44 22 16 16 44 33 81 81 444 256 256 4 445 625 625 5
44 4 4 xx x x
42 8 8 24x xx x
43 12 12 34x xx x
Divide exponent by 4.
Simplifying Radicals (finding roots)nth
Example 1
Simplify the following radicals
169
13
Example 229x
29 x3x
Example 39 153 27c y
3 9 153 327 c y 3 53c y
Example 43 63 8x y
3 3 63 38 x y 22xy
.
a. b. c. d.
0 000
a. b. c. d.
.A
.B
Target Goal: Simplify Radicals.
.C
.D
4 124 16x y
64xy
2 64x y
32xy
42xy
Simplify.
Response Grid
Countdown
15
.
a. b. c. d.
0 000
a. b. c. d.
.A
.B
Target Goal: Simplify Radicals.
.C
.D
3 9 36125a b
3 125a b
3 65a b
3 625a b
3 125a b
Simplify.
Response Grid
Countdown
15
Simplifying Radicals (finding roots)nth
Example 5
Simplify the following radicals
55 4x
4x
Example 62 2 1x x
1 1x x
21x
1x
.
a. b. c. d.
0 000
a. b. c. d.
.A
.B
Target Goal: Simplify Radicals.
.C
.D
24 4 1x x
1x
2 1x
22 2 1x x
4 1x
Simplify.
Response Grid
Countdown
15
Use a Calculator to Approximate RadicalsApproximate each of the following radicals using a calculator
Example 7
122
Example 83 339
Example 95 837
11.045 6.973 3.842
Team Scores100 Team 10100 Team 666.67 Team 366.67 Team 160 Team 550 Team 825 Team 425 Team 20 Team 70 Team 9
End
Advanced Algebra / Trigonometry
Section 7-4nth Roots
Target Goals
1) Simplify Radicals2) Use a Calculator to Approximate
Radicals
Simplifying Radicals (finding roots)nth
Vocab
Review
Square Root:
The root that you've already worked with is the 2nd root.nth
:Ex 49 7
2For any real numbers and , if , then is the square root of .a b a b a b
The 2nd root is usually called the "square root" and is denoted with the symbol, .
7 is the principal (positive) square root of 49.
49 7 7 is the opposite of the principal square root of 49.
49 7 7 represent both square roots of 49.
Simplifying Radicals (finding roots)nthNew
5th roots, etc.
** An even root of a positive number will have a positive and negative answer.
Now we will be working with 3rd roots "cube roots", 4th roots,
Vocab
Unless indicated, we will only write the positive (principal) root.
** An odd root of a positive number will have a positive answer.
4 256 4:Ex
The th root is denoted with the symbo l .nn
5 32 2 3 27 3
** An even root of a negative number is a non-real solution (will talk about later).
** An odd root of a negative number will have a negative answer.
4 16 2
Perfect Squares21 11 1
22 44 2 23 99 3
2 6 44 16 1 2 5 55 25 2 2 6 66 36 3 2 9 77 49 4 2 4 88 64 6 2 1 99 81 8
210 10 10 100 0 211 12 11 121 1 212 14 14 144 2 213 16 19 169 3 214 19 16 196 4 215 22 15 225 5
22 2 xx x x
22 4 4 2x x x x
23 6 6 3x x x x
Divide exponent by 2.
Perfect Cubes33 11 1 1 33 3 3 xx x x
Divide exponent by 3.
33 22 8 8 33 33 27 27 33 44 64 64 335 125 125 5 336 216 216 6 337 343 343 7 338 512 512 8 339 729 729 9
3 310 1000 1000 10
32 6 3 6 2x xx x
33 9 3 9 3x xx x
Perfect Quads44 11 1 1 44 22 16 16 44 33 81 81 444 256 256 4 445 625 625 5
44 4 4 xx x x
42 8 8 24x xx x
43 12 12 34x xx x
Divide exponent by 4.
Simplifying Radicals (finding roots)nth
Example 1
Simplify the following radicals
169
Example 229x
Example 39 153 27c y
Example 43 63 8x y
Simplifying Radicals (finding roots)nth
Example 5
Simplify the following radicals
55 4x
Example 62 2 1x x
Use a Calculator to Approximate RadicalsApproximate each of the following radicals using a calculator
Example 7
122
Example 83 339
Example 95 837
