**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 .

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

**B.** It can be simplified to –3.

**C.** It is in simplified form.

**D.** 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*).

**A.** 11 + 4*i*

**B.** 13 – 8*i*

**C.** 13 + 4*i*

**D.** 11 + 8*i*

**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*.

**A.** *x* = 2 or *x* = 8

**B.** *x* = 2

**C.** The two solutions for are complex numbers.

**D.** *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*.

**A.** –41

**B.** 4

**C.** 40

**D.** 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)?

**A.** None of the above.

**B.** It is a right triangle.

**C.** It is isosceles.

**D.** 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?

**A.** The mean is and the standard deviation is 5.

**B.** The mean is and the standard deviation is approximately 5.6252.

**C.** The mean is 4.86 and the standard deviation is 5.63.

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