6-4 Study Guide and Intervention PDF

Untitled

10-2 Study Guide and Intervention. Simplifying Radical Expressions. Product When you simplify radical expressions with variables use absolute value to ensure.

Untitled

10-2 Study Guide and Intervention. Operations with Radical Expressions. Add Multiply Radical Expressions Multiplying two radical expressions with different.

10-2 - Study Guide and Intervention

When you simplify radical expressions with variables use absolute value to ensure 16. √ 8. −. 2 √ 7 + 4 √. 10. 4√ 5 - √. 14. −. 33. 10-2. Quotient ...

10-3 - Study Guide and Intervention

Multiply Radical Expressions Multiplying two radical expressions with different (2 - 4 √ 2 )(2 + 4 √ 2 ) - 28. 6. (3 + √ 6 ) 2. 15 + 6√ 6. 7. (2 - 2 √ 5 ) ...

10-4 - Study Guide and Intervention

Radical Equations Equations containing radicals with variables in the radicand are 4x - 7 + 7 = 25 + 7 Add 7 to each side. 4x = 32. Simplify. x = 8. Divide ...

Chapter 10 Resource Masters

.............................. 10. Lesson 10-2. Simplifying Radical Expressions. Study Guide and Intervention ...........................11. Skills Practice ...

6-6 Study Guide and Intervention

Write each expression in radical form or write each radical in exponential form. 1. 11. 1−. 7. 2. 15. 1−. 3. 3. 300. 3−. 2. 4. √. 47. 5. 3√ 3a5b2. 6. 4√

Untitled

Glencoe Algebra 1. Lesson 10-2. Page 4. NAME. DATE. PERIOD. 10-2 Study Guide and Intervention (continued). Simplifying Radical Expressions. Quotient Property of

Chapter 7 Resource Masters

Study Guide and Intervention . . . . . . . . . . . . . .6. Skills Practice 5 and 7 5 are (like radical expressions conjugates). 7. When no index is given ...

Untitled

11-2 Study Guide and Intervention. Operations with Radical Expressions. Add and Subtract Radical Expressions When adding or subtracting radical 4√6. 10√6 – ...

10-2 - Study Guide and Intervention

When you simplify radical expressions with variables use absolute value to Simplify each expression. 1. ?. 28. 2. ?. 68. 3. ?. 60. 4. ?. 75. 2 ? 7.

Untitled

10-2 Study Guide and Intervention When you simplify radical expressions with variables use absolute value to ... 21) 3??72 – 3??72 – 2??6+4??7.

6-6 Study Guide and Intervention

3? 3a5b2. 6. 4? 162p5. Evaluate each expression. 7. -27 Example 2. 6-6 Study Guide and Intervention. Rational Exponents. 7?.

6-4 Study Guide and Intervention

Simplify Radicals. Simplify ? 49z8. 6-4 Study Guide and Intervention nth Roots. Example 1. Example 2. 9. -7 ... Approximate Radicals with a Calculator.

6-6 Study Guide and Intervention - Rational Exponents

6-6 Study Guide and Intervention. Rational Rational Exponents and Radicals ... 4. ?47. 5. ?3 5 2. 3. 6. ?162 5. 4. Evaluate each expression. 7.

10-3 - Study Guide and Intervention

Glencoe Algebra 1. Study Guide and Intervention. Operations with Radical Expressions. Add or Subtract Radical Expressions When adding or subtracting radical.

6-7 Study Guide and Intervention(continued) - Solving Radical

6-7 Study Guide and Intervention(continued). Solving Radical Equations and Inequalities. Solve Radical Inequalities A Now solve 5 – ?20 + 4 ? – 3.

7-3 - Study Guide and Intervention

Rational Exponents For any real numbers a and b and any positive integer n if an = b

Chapter 10 Resource Masters

4. Lesson 10-1. Square Root Functions. Study Guide and Intervention . Before multiplying two radical expressions with different.

Untitled

Step 4. Study Guide and Intervention. Radical Equations and Inequalities x = 7. Isolate the radical on one side of the equation.

Lesson 6-4

NAME DATE PERIOD

PDF Pass

Chapter 6 25 Glencoe Algebra 2

Simplify Radicals

Simplify

49z
8 49z
8 (7z 4 2 = 7z 4 z 4 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

Exercises

Simplify.

1. ⎷ ?? 81 2. 3 ⎷ ??? -343 3. ⎷ 144p
6

4. ±

4a 10 5. 5 243 p
10 6. - 3 m 6 n 9 7. 3 -b 12 8. 16a 10 b 8 9. 121x
6 10. (4k) 4

11. ±

169r
4 12. - 3 -27 p 6 13. - 625y
2 z 4

14. ⎷

36q
34

15. ⎷

100x
2 y 4 z 6 16. 3 ⎷ ??? -0.027 17. - ⎷ ??? -0.36 18. ⎷ 0.64p 10 19. 4 (2x) 8

20. ⎷

(11y 2 4 21.
3 (5 a2 b 6 22.
(3x - 1) 2 23.
3 (m - 5) 6

24. ⎷ ??????

36x
2 - 12x + 1

Square RootFor any real numbers a and b, if a

2 = b, then a is a square root of b. nth RootFor any real numbers a and b , and any positive integer n , if an = b, then a is an nth 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.

6-4Study Guide and Intervention

n th Roots

Example 1Example 2

9 -7 12

p 3

±2a

5 3p 2 -m 2 n 3 -b 4 4 a 5 b 4 11 x 3 16k 2

±13r

2 3p 2 -25 y z 2 6 q 17 10 x y 2 z 3 -0.3 not a real number 0.8| p 5 4x 2 121y
4 25a
4 b 2 |3x - 1| (m - 5) 2 |6x - 1|

021_030_ALG2_A_CRM_C06_CR_660551.indd 25

021_030_ALG2_A_CRM_C06_CR_660551.indd 2512/28/10 10:32 AM12/28/10 10:32 AM

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

18.2 to three decimal places.

5 ⎷ ?? 18.2 ≈ 1.787

Exercises

Use 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 + h

2 . What is the distance to the horizon if a satellite is orbiting 150 miles above Earth? Irrational Numbera number that cannot be expressed as a terminating or a repeating decimal

Study Guide and Intervention (continued)

n th 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

021_030_ALG2_A_CRM_C06_CR_660551.indd 26021_030_ALG2_A_CRM_C06_CR_660551.indd 2612/20/10 9:21 PM12/20/10 9:21 PM

quotesdbs_dbs9.pdfusesText_15

[PDF] 6-4 Study Guide and Intervention

Lesson 6-4

NAME DATE PERIOD

PDF Pass

Chapter 6 25 Glencoe Algebra 2

Simplify Radicals

Simplify

Exercises

Simplify.

4. ±

11. ±

14. ⎷

15. ⎷

20. ⎷

24. ⎷ ??????

Square RootFor any real numbers a and b, if a

Real nth Roots of 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.

6-4Study Guide and Intervention

Example 1Example 2

9 -7 12

±2a

±13r

021_030_ALG2_A_CRM_C06_CR_660551.indd 25

021_030_ALG2_A_CRM_C06_CR_660551.indd 2512/28/10 10:32 AM12/28/10 10:32 AM

NAME DATE PERIOD

PDF Pass

Chapter 6 26 Glencoe Algebra 2

Approximate Radicals with a Calculator

Radicals such as

Use a calculator to approximate

18.2 to three decimal places.

Exercises

LAW ENFORCEMENT The formula r = 2

5L is used by police to estimate the speed r

8000h + h

Study Guide and Intervention (continued)

Example

7.874 32.404 0.378

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

021_030_ALG2_A_CRM_C06_CR_660551.indd 26021_030_ALG2_A_CRM_C06_CR_660551.indd 2612/20/10 9:21 PM12/20/10 9:21 PM