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# 1. Which of these expressions is in simplified form? A. a

1. Which of these expressions is in simplified form?
A. a ^3 sqrt 4 - b ^3 sqrt 2 / 2
B. sqrt 1/2x + sqrt 1/2z
C. x^2 - 3x sqrt y / sqrt 3
D. sqrt 125x - x^2
2. Compute the value of |-6 - 6i|
A. 6
B. 12i
C. 6 sqrt2
D. 6 + 6i
3. Simplify (81a^8b^2) ^1/4 *
A. 81a^2b^1/2
B. 3a^2 sqrt |b| *Am pretty sure this is correct
C. 3a^2 sqrt b
D. +3a^2b^2
4. Simplify (6 − i)(2 + i). *? I come up with 12 + 4x - x^2
A. 11 + 4i
B. 13 − 8i
C. 13 + 4i
D. 11 + 8i
5. Rationalize the denominator of 2 / ^3 sqrt a-1. *
A.
B.
C.
D.
6. Solve for 20 - sqrt 3x = 16x.
A. 16/3 *I believe this is correct
B. 12
C. 16/9
D. 5
7. Solve for sqrt 2x + x = 4, solve for x.
A. x = 4 or x = –4
B. x = 2 *I believe this is correct.
C. x = 2 or x = 8
D. The two solutions for are complex numbers.
8. Simplify ^3 sqrt 810.
A. 9 ^3 sqrt 10
B. 81 ^3 sqrt 10
C. 3 ^3 sqrt 30
D. 2 * 5 * ^3 sqrt 81
9. If the hypotenuse of a right triangle is 6m and one side is 4m, what is the length of the other side?
A. 5 sqrt 4
B. -2 sqrt 5
C. 2 sqrt 5 *I believe this is correct
D. 4 sqrt 5
10. 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. None of the above. I believe this is correct
C. It is isosceles.
D. It is a right triangle.
11. To solve for x, begin with which of these steps?
A. Square both sides of the equation. *I believe this is correct
B. Eliminate the negative in the second radical expression.
D. Combine the two like radicals, then square both sides.
12. Expand (x - 2 sqrt y)(x = 2 sqrt y) and simplify. Assume y > = 0
A. x^2 - 4x sqrty + y
B. x ^2 - 4y *I believe this is correct
C. x^2 + 4y
D. x^2 + 4x sqrt y + y
13. Simplify 5 sqrt 2 / 2 - I by rationalizing the denominator.
A. 2 sqrt 2 + 2i sqrt 2 *I believe this is correct
B. 10 / 2 sqrt2 - I sqrt 2
C. 5 sqrt 2 (2 - I) / 3
D. sqrt 2 (2-i)/3
14. Solve for - sqrt 2x + 1 = -9x.
A. 4
B. –41
C. 50
D. 40 * I believe this is correct
15. Rationalize the denominator of sqrt x + sqrt y / sqrt x - sqrt y assuming x ≥ 0 and y ≥ 0.
A. sqrt x - sqrt y / sqrt x + sqrt y
B. x + 2 sqrt xy + y / x - y
C. x^2 + Y^2/x^2 - y^2
D. x + y/x - y *I think this is correct
16. Which of these points is 5 units away from the point (6, –1)?
A. (3,3)
B. (6 + sqrt 2, -1 + sqrt 2) * I think this is right
C. (6 + sqrt 2, 6 - sqrt 2)
D. (0, 5)
17. Which of these expressions simplifies to sqrt 3 (|x| - 5x^2) / 3?
A. sqrt x^2 (1 - 5x)/3 sqrt x
B. sqrt 3 (|x| - 5)x / 3
C.sqrt x^2 (x-5)/3 sqrt x
D. sqrt x^3 - 5 sqrt x^5 / sqrt 3x
18. Simplify ^3 sqrt -16xy^6.
A. 2y^2 ^3 sqrt -2x
B. -4y^2 ^3 sqrt x
C. 2y^2 ^3 sqrt -x
D. -2y^2 ^3 sqrt 2x
19. 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, because city blocks are much smaller than one quarter of a mile.
B. No, but if the turn were to the left instead, they would be within range.
C. Yes, as the distance formula indicates. * I believe this is correct.
D. No, because the distance is greater than 1320 feet.
20. Simplify (^4 sqrt 16x^4y^5)(^4 sqrt 243y^7) assuming the variables represent non-negative numbers.
A. 6^4 sqrt 3 xy^3
B. 6xy^3
C. 2xy^4 sqrt y 3^4 ^4 sqrt 3 y^4 sqrt y^3
D. 6x^2Y^2 ^4 sqrt 3
21. Which expression has the same value as 25½?
A. 125 2/3
B. 25 1/3
C. -5
D. sqrt (-5)^2
22. Expand (sqrt c = sqrt d)^2and simplify. Assume c ≥ 0 and d ≥ 0.
A. c + 2 sqrt cd + d
B. c^2 + 2cd + d^2
C. |c| + 2|cd| + |d| * I think this is correct
D. c^2 - d^2
23. Choose the best description of the radical expression ^3 sqrt -9 .
A. It can be simplified to - ^3 sqrt 9, but no further.
B. It can be simplified to –3. *I think this is correct
C. It can be simplified, but the result is a complex number.
D. It is in simplified form.
24. Combine like radicals in ^5 sqrt 2x - ^5 sqrt 32x^5 + ^5 sqrt -64x + ^3 sqrt 8x^3.
A. ^5 sqrt 2x - 4x
B. ^5 sqrt 2x
C. -^5 sqrt 2x + 4x
D. _ ^5 sqrt 2x
25. Which of these radical expressions simplifies to x?
A. sqrt -x
B.(sqrtx)^2 I think this is right.
C. sqrt x / x
D. sqrt x^2

Thank you! Please let me know what I owe!

JACUSTOMER-yrynbdjl- :

I would like to work on this. When do you need an answer . What is your deadline?

Customer:

By Monday if possible. Thank you so much!

JACUSTOMER-yrynbdjl- :

That should be no problem. I will be bacjk to you well before this deadline.

Customer:

Thanks again!

You are very welcome.So far I am having trouble reading question 5.
Customer: replied 3 years ago.

Rationalize the denominator of 2 / power 3 sqrt of a - 1. hope that helps

Thank you.

2/cube root of (a-1)?

Is that what this expression means?
Please resend Problems 6 &14. I am having trouble interpreting the notation used. Otherwise here is my solution file-Please copy and Paste in your browser
https://www.box.com/s/tvm6p7v3z9na5hfb28kb

Here is the backup analysis of each question so you know how I came up with the answers

https://www.box.com/s/5vd7qp0g5gg9po7l30uo

Please get back to me with any questions you have.

I believe I found the typo in problems 6 & 14
https://www.box.com/s/jmr1r7yxzmkox06kkmyt

I still need your help with the expression in problem
21 )

(125)^(2/3)=5^2=25 ?
Customer: replied 3 years ago.

#5 is: 2 / power of 3 sqrt of a-1.

#21 is: Which expression has the same value as 25 1/2?

a. 125 2/3

b. 25 1/3

c. -5

d. sqrt (-5)^2

Hi
in #21
25 1/2 does that mean 25 to the power (1/2)? Sorry but I am still having trouble with the notation.

Customer: replied 3 years ago.

I apologize but it would be extremely helpful if you told me in words what 25 1/2 means since none of the answers is the number 25 1/2 or the decimal 25.5.
Customer: replied 3 years ago.

No problem - I don't understand it either! This is verbatium:

Which expression has the same value as twenty five and one half?

a. one hundred twenty five and two thirds

b. twenty five and one third

c. negative five

d. square root of negative five squared

I believe there is a typo here. I believe the question might be "which expression has the same value as -25^(1/2)and the answer is c) -5. I hope this helps you and any questions you have are more than welcome. Just ask for Len and a bonus would be more than appreciated.