Questions on Algebra: Radicals -- complicated equations involving roots answered by real tutors!

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Algebra: Radicals -- complicated equations involving roots

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Question 43092: How would you explain square roots, cube roots, nth roots, and radicals to a student who is having difficulty understanding these concepts? What are some limitations of square root?

Thank you!
Click here to see answer by josmiceli(3012)

Question 43343: Multiply as indicated. Please help!
(1 + sqrt2)^2
Click here to see answer by stanbon(26284)

Question 43343: Multiply as indicated. Please help!
(1 + sqrt2)^2
Click here to see answer by checkley71(8405)

Question 43341: I have to find the indicated root or state that the expression is not a real number. Can you please tell me if I'm right?
The problem is:
-4th root Sqrt81
I can't find anywhere that it says if the root number is negative whether or not it is a real number. If I multiply negative 3 out 4 times I get 81. Please help!
Click here to see answer by stanbon(26284)

Question 43346: Stan,
To explain the problem you are unsure of (what I'm asking) is:
The problem would look like the fourth root of 81. However, there is a negative sign in front of the 4.
Does that help?
Click here to see answer by stanbon(26284)

Question 43345This question is from textbook

: hello, I need to rationalize the denominator to the following: square root of 3x divided by square root of x minus square root of 3. Thank you for your time!
This question is from textbook

Click here to see answer by stanbon(26284)

Question 43422: I really need help with this one...no one has provided an answer yet. I would really, really appreciate it. I'm stuck...
all positive real numbers and put in simplified form
4th root of 5y/3x^3
Click here to see answer by stanbon(26284)

Question 43444This question is from textbook

: Hello, I need to factor the following polynomial: x squared minus 5. Thank you for your time.This question is from textbook

Click here to see answer by fractalier(1804)

Question 43443This question is from textbook

: Hello, I need to simplify the following expression: square root of 20 divided by square root of 15. Thanks!This question is from textbook

Click here to see answer by fractalier(1804)

Question 43448This question is from textbook

: Hello, I need to simplify the following expression: square root of 16a^4x^2. Thanks!This question is from textbook

Click here to see answer by fractalier(1804)

Question 43493: How to solve the following equation:
_
/x-1=3 _
(This / symbol is for square root)
Click here to see answer by stanbon(26284)

Question 43485: Find the value of the discriminant for 9x^2+1=6x. Then describe the number and type of roots for the equation.
Thanks
Click here to see answer by Nate(3495)

Question 43555: Working on Radicals...
sqrt x^3 = 8: would x be 2? can you please show me step by step? thanks!
3sqrt x^2 = 4: not sure of this one.. the 3 is throwing me; again step by step, it's the only way I can truly understand all this. thanks again!!
Click here to see answer by checkley71(8405)

Question 43566: Use completing the square or the quadradic formula to find the solutions to the equation: x^2-4x+2=0. Thank you for your time.
Click here to see answer by aaaaaaaa(138)

Question 43578: Solve the equation: x+2-2 sqrt of x+2 =0
The answer is one of the following: A.x=-2,2 B.x=-2,0 C.x=4 D.x=4,8
Thank you!
Click here to see answer by Nate(3495)

Question 43633: Hello, Here is another problem I had some trouble with today. I tried to work through it, but would appreciate any help that could be provided.
Question,
4√[50] + √[32] – √[18]
My Work
5√2+4√2-3√2
9√2-3√2
6√2
Not sure if I did this right or not, but would appreciate some confirmation, or any help someone could provide.
Thanks...
Click here to see answer by Nate(3495)

Question 43638: Hello, Here is another problem I had some trouble with today. I tried to work through it, but would appreciate any help that could be provided.
Question,
4√[50] + √[32] – √[18]
My Work
5√2+4√2-3√2
9√2-3√2
6√2
Not sure if I did this right or not, but would appreciate some confirmation, or any help someone could provide.
Thanks...
Click here to see answer by Nate(3495)

Question 43642: Hello, hopefully my last question for the day. I have read the textbook and do not understand how to rationalize the denominator for the following question. Can someone please walk me through the steps to do this.
7
___________
√[3] – √[2]
Thanks
Click here to see answer by Nate(3495)

Question 43640: Hello, I am really having trouble with these radical expressions. Here is another one I cannot solve. I think I should use the foil method, but am not sure I am doing it right, can someone please help me..
(5√[3]+√[5])(√[3]–2√[5])
Here I tried to put it together but am just totally stuck at this point. I think I combined them the right way, but I just do not understand how to proceed from here.
5√3√3-5√32√5+√5√3-2√5√5
Any help that can be provided will be greatly appreciated.
Thanks....
Click here to see answer by Nate(3495)

Question 43630: Hello,
I am having trouble with this simplification. I have tried following the textbook, but just do not understand the steps. I would appreciate it if someone could help me out with it.
√[121x^12y^16z^6] Original Question
Here is what I came up with when I tried to do it.
11√x^12y^16z^6
11√x^6y^8z^3
Not sure if this is right or not, but am looking for some help on getting to the correct spot.
Thanks,
Click here to see answer by Nate(3495)

Question 43652: Use completing the square or the quadradic formula to find the solutions to the equation: x^2-4x+2=0. I am stuck on this one, thank you in advance for any help.
Click here to see answer by tutorcecilia(2042)

Question 43899: I am stuck.
x^2=-6x
Click here to see answer by stanbon(26284)

Question 43924This question is from textbook Algebra and Trigonometry with Analytic Geometey

: Find all roots of the polynomial x^3-x^2+16x-16. My answer is -1,4i,-4i is this right. thanks for looking at this problem.This question is from textbook Algebra and Trigonometry with Analytic Geometey

Click here to see answer by longjonsilver(2297)

Question 43924This question is from textbook Algebra and Trigonometry with Analytic Geometey

Click here to see answer by tutorcecilia(2042)

Question 43891: how to solve radicals equations involving roots
Click here to see answer by fractalier(1804)

Question 43974This question is from textbook

: I am extremely frustrated. I cannot get to any of my multiple choice answers.
-16X^3 +-32X^2
-32X^2 + -16X^3
-16X2(2 + X)
answer options
A: 8x^2(-2x - 32)
B: 8x^2(-2x - 4)
C: -16x^2(x - 32)
D: -16x(x^2 - 32x)
Can someone help me?
This question is from textbook

Click here to see answer by adamchapman(301)

Question 43974This question is from textbook

Click here to see answer by grohrbach(2)

Question 44013: I would really appreciate some help with these equations
Determine whether -^4 sqrt16 is rational or irrational
Click here to see answer by adamchapman(301)

Question 44015: Evaluate if possible
-^3 sqrt64
I come up with -4, is that correct?
Click here to see answer by adamchapman(301)

Question 44182: Help. I need answers with work shown for the following 2 problems:
Use the Product Rule for radicals to simplify each expression. All variables represent nonnegative real numbers.
³√5b^9
(* It's hard to write this problem as it appears because this site is limited and doesn't allow for pasting, but in the book the 3 is in the V of the SQ root and the 5b^9 is under the arm.)

Use the product rule to simplify.
60. 4√32 (same on this one, the 4 is in the V and 32 under the arm)

Click here to see answer by stanbon(26284)

Question 44218: Sorry but this one is hard to write and I am lost
Find the perimeter of a triangle with sides
4
square root of 5 minus the square root of 3
square root of 5 plus the square root of 3

Click here to see answer by adamchapman(301)

Question 44246: Find the time required for an ojbect to fall to ground from the building is 1400 Ft high. t=1/4 square root is s.
Click here to see answer by fractalier(1804)

Question 44333: Reduce each expression to the lowest terms. Show steps and solution.
This is written in fraction form:
4x^2/2x^9
Click here to see answer by fractalier(1804)

Question 44354: Can someone help me with this problem. I have to determine this is rational or irrational.
the negative symbol is alone to the left with the number 4 raised.
___
-4√16
I believe this is irrational
Click here to see answer by adamchapman(301)

Question 44383: simplify by combining like terms.
question 32. ^63-2^28+5^7
I don't have the signs on my computer for square roots.
it is square root of 63, square root of 28, and square 7.
Click here to see answer by fractalier(1804)

Question 44694: Is my answer correct?
Find the area of the rectangle L=sqrt3+sqrt5 W=sqrt3+sqrt5 Area=LW
This would give me: sqrt3+sqrt5 multiplied by sqrt3+sqrt5
I would then apply the foil method which gives me:
sqrt9 + sqrt15 +sqrt15 + sqrt25
this equals
3 + sqrt15 + sqrt15 + 5
which gives me
8 + 2sqrt15 as the final answer. Is this correct?
Click here to see answer by stanbon(26284)

Question 44747: find the length x in the triangle and express in simplified radical form
sides of the triangle are 10, 8, and x
I get x^2 = 8^2 + 10^2 = 64 + 100 = 164
not sure if this is correct and I think I am missing the final step.
Thanks for help
Click here to see answer by fractalier(1804)

Question 43446This question is from textbook

: Hello, I need to simplify the following expression: 1/x-1/b divided by 1/xb+1/2. Thank you!This question is from textbook

Click here to see answer by Rekham(3)

Question 43446This question is from textbook

: Hello, I need to simplify the following expression: 1/x-1/b divided by 1/xb+1/2. Thank you!This question is from textbook

Click here to see answer by OHtutor(16)

Question 44795: I have to simplify by combinineg like terms
(s.r. of 3 + 5)(s.r. of 3 - 3)
Do I start with the FOIL method? If so - it doesn't look right?
Thanks
Click here to see answer by stanbon(26284)

Question 44929: I am required to solve using the quadratic formula, if there are no real roots, then that can be an answer too. Thank you.
3=7x-4x(2) the two in parentheses is a power.
Click here to see answer by venugopalramana(3286)

Question 44947: Can someone help with this question?
The shape of a supporting arch can be modeled by h(x)=-0.03x^2+3x, where h(x) represents the height of the arch and x represents the horizontal distance from one end of the base of the arch in meters. Find the maximum height of the arch.
Click here to see answer by Nate(3495)

Question 44944: Simplify:
√16x^2y^4
Click here to see answer by tutorcecilia(2042)

Question 44945: Simplify:
(√12)-(√18)+(3√50)+(√75)
Click here to see answer by tutorcecilia(2042)

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