Download 6-4 Study Guide and Intervention

NAME
DATE
6-4
PERIOD
Study Guide and Intervention
nth Roots
Simplify Radicals
Square Root
For any real numbers a and b, if a 2 = b, then a is a square root of b.
nth Root
For any real numbers a and b, and any positive integer n, if a n = b, then a is an nth
root of b.
Real n th Roots of b,
1. If n is even and b > 0, then b has one positive real root and one real negative root.
n
n
√
b , - √
b
2. If n is odd and b > 0, then b has one positive real root.
3. If n is even and b < 0, then b has no real roots.
4. If n is odd and b < 0, then b has one negative real root.
Example 1
Example 2
Simplify √
49z8 .
3
4 2
√
49z8 = √(7z
) = 7z4
z4 must be positive, so there is no need to
take the absolute value.
3
(2a - 1)6
Simplify - √
3
- √
(2a - 1)6 = - √
[(2a - 1)2]3 = -(2a - 1)2
Exercises
Simplify.
3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9
4a10
4. ± √
±2a 5
3
12
7. √-b
-b4
4
10. √(4k)
16k 2
5.
4x 2
(3x - 1)2
22. √
|3x - 1|
Chapter 6
-m 2n 3
10 8
8. √16a
b
6
9. √121x
4|a 5|b4
11|x 3|
3
12. - √
-27p 6
11. ± √
169r4
±13r 2
6 | q17|
4
(2x)8
19. √
6. - √
m6n9
3p 2
-25|y | z 2
-0.3
3
5
243p 10
√
14. √
36q34
3
12|p 3|
-7
625y2z4
13. - √
-0.027
16. √
6
3. √144p
2. √
-343
3p 2
15. √
100x2y4z6
10|x | y 2| z 3|
10
18. √0.64p
17. - √
-0.36
not a real number
0.8 | p 5|
3
21. √
(5a2b)6
20. √
(11y2)4
121y 4
25a 4b 2
3
23. √
(m - 5)6
24. √
36x2 - 12x + 1
|6x - 1|
(m - 5)2
25
Glencoe Algebra 2
Lesson 6-4
1. √
81
NAME
DATE
6-4
Study Guide and Intervention
PERIOD
(continued)
nth Roots
Approximate Radicals with a Calculator
Irrational Number
a number that cannot be expressed as a terminating or a repeating decimal
and √
Radicals such as √2
3 are examples of irrational numbers. Decimal approximations
for irrational numbers are often used in applications. These approximations can be easily
found with a calculator.
Example
5
18.2 to three decimal places.
Use a calculator to approximate √
5
√
18.2 ≈ 1.787
Exercises
Use a calculator to approximate each value to three decimal places.
1. √62
7.874
4
4. - √
5.45
-1.528
0.308
6
10. √856
3.081
32.404
5. √
5280
3
5
9. √
100
-2.466
2.512
11. √
3200
12. √
0.05
56.569
111.803
0.775
0.531
136.382
8. √
-15
14. √
0.60
3
6. √
18,600
72.664
13. √
12,500
16. √
0.15
0.378
0.224
4
15. - √
500
-4.729
6
17. √
4200
18. √
75
4.017
8.660
is used by police to estimate the speed r
19. LAW ENFORCEMENT The formula r = 2 √5L
in miles per hour of a car if the length L of the car’s skid mark is measures in feet.
Estimate to the nearest tenth of a mile per hour the speed of a car that leaves a skid
mark 300 feet long. 77.5 mi/h
20. SPACE TRAVEL The distance to the horizon d miles from a satellite orbiting h miles
8000h + h2 . What is the distance to the
above Earth can be approximated by d = √
horizon if a satellite is orbiting 150 miles above Earth? about 1100 mi
Chapter 6
26
Glencoe Algebra 2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
7. √0.095
3
3. √
0.054
2. √
1050