Pf exam radicals and rational exponents

Pf exam radicals and rational exponents

Exam: 050294RR – Radicals and Rational Exponents

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1. Simplify  by rationalizing the denominator.

2. 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  and the standard deviation is approximately 5.6252.

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

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

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

4. Which of these radical expressions simplifies to x?

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

A. It has area 22 square units.

B. It is isosceles.

C. None of the above.

D. It is a right triangle.

6. Which of the following best describes imaginary numbers?

A. They are the complex numbers.

B. They consist of two values, the principal imaginary number i and its negative –i.

C. They are the values of expressions of the form  for various real numbers a, as long as a ≠ 0.

D. They are not numbers, but are useful in solving equations.

7. Expand  and simplify. Assume y = 0.

8. 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. Yes, as the distance formula indicates.

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

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

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

9. Simplify .

10. Rationalize the denominator of .

11. Simplify (6 – i)(2 + i).

A. 13 – 8i

B. 13 + 4i

C. 11 + 8i

D. 11 + 4i

12. Compute the value of .

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

14. Simplify i

A. 1

B. –1

C. –i

D. i



15. Which of these expressions is in simplified form?

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

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. Solve  for x.

A. x = 2

B. The two solutions for are complex numbers.

C. x = 2 or x = 8

D. x = 4 or x = –4

20. Simplify .

21. Solve  for x.

22. To solve  for x, begin with which of these steps?

A. Isolate one radical expression.

B. Combine the two like radicals, then square both sides.

C. Square both sides of the equation.

D. Eliminate the negative in the second radical expression.

23. Simplify .

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

25. Combine like radicals in .

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