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

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Question 712873: Simplify by factoring, type in exact answer using radicals as needed.
√40
Click here to see answer by jim_thompson5910(35256)

Question 713229: multiply
(square root of 11 minus 3)(square root of 11 minus 3)
I FOIL and get square root of 11 times square root of 11 minus 3 square root of 11 minus 3 square root of 11 plus 9.
then i simplify and get 11 minus 6 square root of 11 plus 9
then i subtract 11 to both sides and get
-6 square root of 11 minus 2
Click here to see answer by ankor@dixie-net.com(22740)

Question 712657: √5-√3-√2 over √5+√3+√2 please help me solve
Click here to see answer by jsmallt9(3758)

Question 714222: I have done this problem but i don't know what the correct answer is please help
the problem is
Please answer(:
Click here to see answer by ankor@dixie-net.com(22740)

Question 714665: Hi, I need some help with this one.. I don't understand what to do.
(-3 sqrt2)(4 sqrt6)
Click here to see answer by stanbon(75887)

Question 714933: How do you multiply radicals? For example -4radical15 multiplyed by -radical3
Click here to see answer by Alan3354(69443)

Question 715242: ABCD is a square. The length of the diagonal is 10√ ̅2. Find the perimeter of the sqare.
Click here to see answer by mananth(16946)

Question 715508: simplify the cubed root of 125(x+4)^3
Click here to see answer by josmiceli(19441)

Question 715617: what is the numerical value of 4 raise to onethird?
what is the numerical value of 32 raise to negative three halves?
what is the numerical value of (18/81) raise to three fourths?
what is the numerical value of (-32) raise to negative two fifth?

Click here to see answer by jsmallt9(3758)

Question 715740: Can a function with the complex roots 5,sqrt(2), and 3i be a fourth-degree polynomial with rational coefficients? Explain.
Click here to see answer by josgarithmetic(39617)

Question 715742: Use the rational root theorem to list all possible rational roots for each equation.then find any actual roots.
1). X^4-7x^2+12=0
Click here to see answer by KMST(5328)

Question 715790: Rationalize the denominator
(3-Sqrt(6))/(x-(3+Sqrt(6)))
Answer should be (3x-15+6Sqrt(6)-xSqrt(6))/(x^2-6x+3) but i don't see how they are getting that answer. please explain
Click here to see answer by jsmallt9(3758)

Question 716206: Not even sure what kind of problem it is. Sorry.
If s is a positive integer, what is the least value of s for which √7s/4 is an integer?

Click here to see answer by jim_thompson5910(35256)

Question 716784: I need help with this

√21/49
Click here to see answer by checkley79(3341)

Question 717181: please help me solve this equation 3√(x-2)-2√(x-5)=4
Click here to see answer by stanbon(75887)

Question 717301: What is the extraneous solution of sqrt(x-3)= (x-5)
also sqrt of(x+4)=sqrt(3x)
Click here to see answer by jsmallt9(3758)

Question 717542: what is 512^-1/3 convert into radical notation

Click here to see answer by jsmallt9(3758)

Question 717491: Simplify the radical.
square root of 5/36
Click here to see answer by jsmallt9(3758)

Question 717955: x-2 = square root 3x-8
Click here to see answer by oscargut(2103)

Question 717946: square root of 40 minus the square root of 10
Click here to see answer by oscargut(2103)

Question 717978: 2(radical sign))54

and -2(radical sign) 6a^3 multiply (radical sign)3a

When you have a number infront of the radical what do you do? and say you simplify a radical and then the answer has a number infront of the radical do you keep it or do you have to simplify it more like these problems?
Click here to see answer by Alan3354(69443)

Question 718113: How can you round 20 over radical 2?
Click here to see answer by Alan3354(69443)

Question 718129: Simplify the following expressions.
(a)
(b)
Click here to see answer by DrBeeee(684)

Question 718191: (Quartic root sign over 18)�(square root 12)
Click here to see answer by jsmallt9(3758)

Question 718135: For what values of x is a true statement? Assume a >= 0.
Click here to see answer by jsmallt9(3758)

Question 718131: Rationalize the numerator for the following expression.
(a)
(b)
Click here to see answer by jsmallt9(3758)

Question 718452: Please help me solve this equation: sqrt810+sqrt240-sqrt250
Click here to see answer by Alan3354(69443)

Question 718452: Please help me solve this equation: sqrt810+sqrt240-sqrt250
Click here to see answer by rfer(16322)

Question 718471: Please help me simplify this equation: 6sqrt20+8sqrt5-5sqrt45
Click here to see answer by mananth(16946)

Question 718567: For what conditions the values a and b is a true statement?
Discuss.
Click here to see answer by jsmallt9(3758)

Question 718459: Please help me simplify this equation: sqrt810+sqrt240-sqrt250
Click here to see answer by jsmallt9(3758)

Question 719061: How do you do this problem? The square root of (2) + the square root of (2/9)?
I know the answer is 4 square root of 2 over 3 but i don't know how they got that answer...
Click here to see answer by god2012(113)

Question 719069: How do I do this problem? The square root of n^2/m^3
Click here to see answer by god2012(113)

Question 719076: How do I answer this question?
3 sqrt of 2 + sqrt of 32
Click here to see answer by KMST(5328)

Question 719087: How do I solve this problem?
(Sqrt of 3 + sqrt of 5)(sqrt of 3 + sqrt of 5)
This is multiplication...
Click here to see answer by jsmallt9(3758)

Question 719166: x+9 under a rad then=x
Click here to see answer by lynnlo(4176)

Question 719250: how would you be able to answer this kind of equation. i have been having trouble with these. can you try explaning with this equasion? 49(radical on it)/54(radical around it)
Click here to see answer by josgarithmetic(39617)

Question 719333: 2 radical x = radical (x+2)
I have no idea how to do this.
Click here to see answer by graphmatics(170)

Question 719384: The solution of
sqrt(x+4)= x-2 ==> x=0 and x=5
x=5 is true since by substituting in the original equation yield 3=3
However,for x=0 we have sqrt(4)=-2 which give an incorrect solution... If we ignore the negative value of squrt(4).
My question is.. Why the negative value is ignored?
Click here to see answer by jsmallt9(3758)

Question 719884: How is this done ?
1.) x^-6y^3/-27x^9y^-3/4
Click here to see answer by lynnlo(4176)

Question 719952: √(2x+17)=x+7
Click here to see answer by lynnlo(4176)

Question 720022: A bird leaves its nest in NY. it flies 6 km due east and 3 km due north how far is the bird from its nest. I dont know if this is a radical the unit we were studying is radical applications. Thank you
Click here to see answer by josmiceli(19441)

Question 720317: Here is my problem.
[SQRT(x + 7)] - 2[SQRT(x)] =-2
OR
√(x + 7) - 2√(x) = -2
-------
Now, the steps I took to solve this problem are to first square both sides:
[√(x + 7) - 2√(x)] * [√(x + 7) - 2√(x)] = 4
so then I FOIL the left side, resulting in:
(x+7) - [√(x + 7) * - 2√(x)] - [ - 2√(x) * √(x + 7)] + 4x
So then I thought to subtract (x+7) and (4x) to both sides
- [√(x + 7) * - 2√(x)] - [ - 2√(x) * √(x + 7)] = 4 - 4x - x - 7 (I think I'm supposed to switch the sign, because I've subtracted it and moved it to the opposite side, right?)
I think I'm correct up to this point, but now I have to square both sides again.
I think this left hand side could be re-written as:
-2[√(x + 7) * - 2√(x)]
Is this right? I'm subtracting it from itself, a negative, which could simply multiplied by -2. Anyway, now I need to square this again, so I assume the -2 becomes a 4 and I FOIL them separately?
FOILING the left side will get:
[√(x + 7) * - 2√(x)] * [√(x + 7) * - 2√(x)]
Which, when FOILed, looks like
(x+7) - [√(x+7) * -2√(x)] - [ - 2√(x) * √(x + 7)] + 4x
It looks exactly the same as before!! I'm just really confused by this problem, and I have a couple more like it, so I want to know if figuring this one out could help me solve the other ones.
I'm confused about FOILing the different sides, whether or not I can combine two square roots, and quite frankly, a lot of other things.
One of the options on the test is 9, and I think this is the answer, because I've inserted it into the original equation and it works, but I'm just confused about how to actually get 9 out of this..
Sorry for the long question. I hope it's not hard to understand. I'm just hoping someone can walk me through all the steps of solving a problem like this so I can do it easily in the future.
Click here to see answer by lwsshak3(11628)

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