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6-4
NAME DATE PERIOD
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Chapter 6 25 Glencoe Algebra 2
Simplify Radicals
Simplify √ �� 49z8 .
√ �� 49z8 = √ ��� (7z4)2 = 7z4
z4 must be positive, so there is no need to take the absolute value.
Simplify - 3 √ ���� (2a - 1)6
- 3 √ ���� (2a - 1)6 = - 3 √ ����� [(2a - 1)2]3 = -(2a - 1)2
ExercisesSimplify.
1. √ �� 81 2. 3 √ ��� -343 3. √ ��� 144p6
4. ± √ �� 4a10 5. 5 √ ��� 243 p 10 6. - 3 √ �� m6n9
7. 3 √ �� -b12 8. √ ��� 16a10b8 9. √ ��� 121x6
10. √ �� (4k)4 11. ± √ ��� 169r4 12. - 3 √ ��� -27 p 6
13. - √ ��� 625y2z4 14. √ ��� 36q34 15. √ ���� 100x2y4z6
16. 3 √ ��� -0.027 17. - √ ��� -0.36 18. √ ��� 0.64p10
19. 4 √ �� (2x)8 20. √ ��� (11y2)4 21. 3 √ ��� (5a2b)6
22. √ ���� (3x - 1)2 23. 3 √ ���� (m - 5)6 24. √ ������ 36x2 - 12x + 1
Square Root For any real numbers a and b, if a2 = b, then a is a square root of b.
nth Root For any real numbers a and b, and any positive integer n, if an = b, then a is an n th
root of b.
Real nth Roots of b,
n √ � b , - n √ � b
1. If n is even and b > 0, then b has one positive real root and one real negative root.
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.
6-4 Study Guide and Interventionnth Roots
Example 1 Example 2
9 -7 12|p3|
±2a5 3p2 -m 2n3
-b4 4|a5|b4 11|x 3|
16k 2 ±13r 2 3p 2
-25|y |z 2 6|q17| 10|x |y 2|z 3|
-0.3 not a real number 0.8|p5|
4x2 121y 4 25a4b2
|3x - 1| (m - 5)2 |6x - 1|
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NAME DATE PERIOD
PDF Pass
Chapter 6 26 Glencoe Algebra 2
Approximate Radicals with a Calculator
Radicals such as √ � 2 and √ � 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.
Use a calculator to approximate 5 √ �� 18.2 to three decimal places.
5 √ �� 18.2 ≈ 1.787
ExercisesUse a calculator to approximate each value to three decimal places.
1. √ �� 62 2. √ �� 1050 3. 3 √ ��� 0.054
4. - 4 √ �� 5.45 5. √ �� 5280 6. √ ��� 18,600
7. √ ��� 0.095 8. 3 √ �� -15 9. 5
√ �� 100
10. 6 √ �� 856 11. √ �� 3200 12. √ �� 0.05
13. √ ��� 12,500 14. √ �� 0.60 15. - 4 √ �� 500
16. 3 √ �� 0.15 17. 6
√ �� 4200 18. √ �� 75
19. LAW ENFORCEMENT The formula r = 2 √ �� 5L is used by police to estimate the speed r 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.
20. SPACE TRAVEL The distance to the horizon d miles from a satellite orbiting h miles above Earth can be approximated by d = √ ����� 8000h + h2 . What is the distance to the
horizon if a satellite is orbiting 150 miles above Earth?
Irrational Number a number that cannot be expressed as a terminating or a repeating decimal
Study Guide and Intervention (continued)
nth Roots
6-4
Example
7.874 32.404 0.378
-1.528 72.664 136.382
0.308 -2.466 2.512
3.081 56.569 0.224
111.803 0.775 -4.729
0.531 4.017 8.660
77.5 mi/h
about 1100 mi
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