Exam: 050294RR – RADICALS AND RATIONAL EXPONENTS

1. Simplify  by rationalizing the denominator.

 

2. Simplify .

 

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

 

4. Choose the best description of the radical expression .
5. It can be simplified, but the result is a complex number.
6. It can be simplified to –3.
7. It is in simplified form.
8. It can be simplified to , but no further.

 

5. Simplify .

 

6. Simplify .

 

7. Rationalize the denominator of .

 

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

 

9. Which expression has the same value as 25½?

 

10. Simplify (6 – i)(2 + i).
11. 11 + 4i
12. 13 – 8i
13. 13 + 4i
14. 11 + 8i

 

11. Which of these expressions simplifies to ?

 

12. Simplify .

 

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

 

14. Combine like radicals in .

 

15. Solve  for x.
16. x = 2 or x = 8
17. x = 2
18. The two solutions for are complex numbers.
19. x = 4 or x = –4

 

 

16. Simplify i

 

17. Simplify  assuming the variables represent non-negative numbers.

 

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

 

19. Which of these radical expressions simplifies to x?

 

20. Solve  for x.
21. –41
22. 4
23. 40
24. 50

 

21. Expand  and simplify. Assume y= 0.

 

22. Solve  for x.

 

23. What best describes the triangle whose corners are located at the points (1, 1), (2, 2), and (0, 16)?
24. None of the above.
25. It is a right triangle.
26. It is isosceles.
27. It has area 22 square units.

 

24. Which of these expressions is in simplified form?

 

25. What are the mean and standard deviation of the data – 6, 12, 2, – 4, 1, 6, 0, 3?
26. The mean is  and the standard deviation is 5.
27. The mean is  and the standard deviation is approximately 5.6252.
28. The mean is 4.86 and the standard deviation is 5.63.

 

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

 

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