# Exam: 050294RR - Radicals and Rational Exponents

Exam: 050294RR - Radicals and Rational Exponents

1. Which of these expressions simplifies to ?

2. Simplify .

3. Simplify (6 - i)(2 + i).

A. 11 + 4i

B. 11 + 8i

C. 13 + 4i

D. 13 - 8i

4. Which of these phrases best describes the standard deviation?

A. It is a measure of variability.

B. It is equal to the mean squared.

C. It increases as more measurements are taken.

D. It is a radical expression using n variables.

5. What are the mean and standard deviation of the data – 6, 12, 2, – 4, 1, 6, 0, 3?

A. The mean is and the standard deviation is approximately 5.6252.

B. The mean is 4.86 and the standard deviation is 5.63.

C. The mean is and the standard deviation is 5.

D. The mean is and the standard deviation is approximately 5.6252.

6. Simplify .

7. Expand and simplify. Assume c = 0 and d = 0.

8. Rationalize the denominator of assuming x = 0 and y = 0.

9. What best describes the triangle whose corners are located at the points (1, 1), (2, 2), and (0, 16)?

A. None of the above.

B. It is isosceles.

C. It has area 22 square units.

D. It is a right triangle.

10. Rationalize the denominator of .

11. Simplify i

A. i

B. 1

C. –1

D. –i

.

12. Which of these expressions is in simplified form?

13. Choose the best description of the radical expression .

A. It is in simplified form.

B. It can be simplified to –3.

C. It can be simplified, but the result is a complex number.

D. It can be simplified to , but no further.

14. Combine like radicals in .

15. Solve for x.

A. x = 4 or x = –4

B. The two solutions for are complex numbers.

C. x = 2

D. x = 2 or x = 8

16. Which of these radical expressions simplifies to x?

17. Solve for x.

18. If the hypotenuse of a right triangle is 6m and one side is 4m, what is the length of the other side?

19. Which of these points is 5 units away from the point (6, –1)?

20. Solve for x.

A. –41

B. 50

C. 40

D. 4

21. Expand and simplify. Assume y = 0.

22. Which expression has the same value as 25½?

23. Two children in nearby houses attempt to use walkie-talkies to communicate. The walkie-talkies reach one quarter of a mile (1320 feet). From one child's house to the other, the walk along the city sidewalks is as follows: Proceed 450 feet from the first house to the nearest corner, turn right 90° and proceed another 1050 feet. Are the children's houses within the 1320-foot range of one another? Choose the best answer.

A. No, but if the turn were to the left instead, they would be within range.

B. Yes, as the distance formula indicates.

C. Yes, because city blocks are much smaller than one quarter of a mile.

D. No, because the distance is greater than 1320 feet.

24. Simplify .

25. Compute the value of .

1. Which of these expressions simplifies to ?

2. Simplify .

3. Simplify (6 - i)(2 + i).

A. 11 + 4i

B. 11 + 8i

C. 13 + 4i

D. 13 - 8i

4. Which of these phrases best describes the standard deviation?

A. It is a measure of variability.

B. It is equal to the mean squared.

C. It increases as more measurements are taken.

D. It is a radical expression using n variables.

5. What are the mean and standard deviation of the data – 6, 12, 2, – 4, 1, 6, 0, 3?

A. The mean is and the standard deviation is approximately 5.6252.

B. The mean is 4.86 and the standard deviation is 5.63.

C. The mean is and the standard deviation is 5.

D. The mean is and the standard deviation is approximately 5.6252.

6. Simplify .

7. Expand and simplify. Assume c = 0 and d = 0.

8. Rationalize the denominator of assuming x = 0 and y = 0.

9. What best describes the triangle whose corners are located at the points (1, 1), (2, 2), and (0, 16)?

A. None of the above.

B. It is isosceles.

C. It has area 22 square units.

D. It is a right triangle.

10. Rationalize the denominator of .

11. Simplify i

A. i

B. 1

C. –1

D. –i

.

12. Which of these expressions is in simplified form?

13. Choose the best description of the radical expression .

A. It is in simplified form.

B. It can be simplified to –3.

C. It can be simplified, but the result is a complex number.

D. It can be simplified to , but no further.

14. Combine like radicals in .

15. Solve for x.

A. x = 4 or x = –4

B. The two solutions for are complex numbers.

C. x = 2

D. x = 2 or x = 8

16. Which of these radical expressions simplifies to x?

17. Solve for x.

18. If the hypotenuse of a right triangle is 6m and one side is 4m, what is the length of the other side?

19. Which of these points is 5 units away from the point (6, –1)?

20. Solve for x.

A. –41

B. 50

C. 40

D. 4

21. Expand and simplify. Assume y = 0.

22. Which expression has the same value as 25½?

23. Two children in nearby houses attempt to use walkie-talkies to communicate. The walkie-talkies reach one quarter of a mile (1320 feet). From one child's house to the other, the walk along the city sidewalks is as follows: Proceed 450 feet from the first house to the nearest corner, turn right 90° and proceed another 1050 feet. Are the children's houses within the 1320-foot range of one another? Choose the best answer.

A. No, but if the turn were to the left instead, they would be within range.

B. Yes, as the distance formula indicates.

C. Yes, because city blocks are much smaller than one quarter of a mile.

D. No, because the distance is greater than 1320 feet.

24. Simplify .

25. Compute the value of .

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