Simplifying Radicals?
965753
sqrt(x) is the same as x^(1/2)\nso Sqrt(x^3y^9) is the same as \n(x^3y^9)^(1/2)\nand this is equal to (x^3)^(1/2) * (y^9)^(1/2).\nNow,\n(x^3)^(1/2)=\nx^(3/2)=\nx*x^(1/2)=\nx sqrt(x)\nand\n(y^9)^(1/2)=\ny^(9/2)=\ny*y*y*y*y^(1/2)=\ny^4 sqrt(y)\nso (x^3)^(1/2)(y^9)^(1/2)=\nxy^4sqrt(xy)
49666
If you are saying simplify then:\nx = The square root of [5x] +2.5\nx = The square root of [5x] +2.5\nx = The square root of [12.5] +2.5\nx = The square root of [12.5] +2.5
478149
-4 (4r^2 + 9) +9 (8r + 2)\nDistributive Propert, (-4)(4r^2)+(-4)(9)+(9)(8r)+(9)(2)\nSimplify, -16r^2-36+72r+18\nCombine like terms, -16r^2+72r-18
889816
1/rt3 *1/rt2-1/rt3\n[1/rt3](1/rt2-1)\n[1/rt3](1-rt2/rt2)\nrationalising\n[(1-rt2)*rt6]/6
674900
When you have (a+b+c)/d, you can separate the terms of the numerator like so a/d + b/d + c/d.  If I do that and simplify, I get:\nx - (6/5) - (3/x).
185700
It's bringing the √2 out from the brackets. \n\nMultiply 1+(3/2) by 2... what do you get? 2+(3)\nMultiply 1+(√3/2) by √2.. what do you get √2+(√3)
752580
It just takes foiling-\n\n(5*2)+(5*5i)+(-3i*2) +(-3i*5i)\n(10)+(25i)+(-6i)+(-15*i^2)\ni^2=-1\nso...\n25+19i\n\nTo those who have said that you can't simplify it past 10 + 19i - 15i^2, that isn't correct considering that since i is the square root of -1, i^2 is -1. That's why you can simplify -15i^2 to 15, thus making it 10+19i+15, or 25+19i
372587
I'm not sure what you are looking for.\n(x-3)/(x+2) does not simplify.\nThe domain is all real numbers except -2.\nThe range is all real numbers except 1.
853794
Evaluate the expression after the ∑ for each of k = 1, 2, ..., up to 6, and add them:\n\n[ 1 + (-1)^1 ] 2^-1 +\n[ 1 + (-1)^2 ] 2^-2 +\n[ 1 + (-1)^3 ] 2^-3 +\n[ 1 + (-1)^4 ] 2^-4 +\n[ 1 + (-1)^5 ] 2^-5 +\n[ 1 + (-1)^6 ] 2^-6\n\nNow use (-1)^1 = -1, (-1)^2 = (-1) × (-1) = 1, ... to get\n\n[ 1 + (-1) ] 2^-1 +\n[ 1 + (1) ] 2^-2 +\n[ 1 + (-1) ] 2^-3 +\n[ 1 + (1) ] 2^-4 +\n[ 1 + (-1) ] 2^-5 +\n[ 1 + (1) ] 2^-6\n\n=\n\n[ 0 ] 2^-1 +\n[ 2 ] 2^-2 +\n[ 0 ] 2^-3 +\n[ 2 ] 2^-4 +\n[ 0 ] 2^-5 +\n[ 2 ] 2^-6\n\n= 2 × 2^-2 + 2 × 2^-4 + 2 × 2^-6\n\nUsing a^m × a^n = a^(m + n), simplify the exponents, to get\n\n2^-1 + 2^-3 + 2^-5 \n= 1 / 2 + 1 / 8 + 1 / 32\n= 16 / 32 + 4 / 32 + 1 / 32 \n= 21 / 32
648070
http://www.anagramgenius.com/archive/algebr.html\n\nedit: sorry didn't answer your real question. I don't know of a program that does what you want, but it shouldn't be too hard to write it. \n\nEdit: Contact me at algebra@envisagecapital.com if you would like the solution. I wrote a quick program to do what you wanted.
179535
I believe it simplifies to n - w.\n\nHere's the expression you wrote: (a-y/w+n * w^2-n^2/y-a).\n\nHere's what I think it should look like:\n\n((a-y)/(w+n)) * ((w^2-n^2)/(y-a))\n\nBecause:\n\n((a-y)/(w+n)) * ((w^2-n^2)/(y-a))\n\n= ((a-y)/(w+n)) * ((w+n)(w-n))/(y-a)\n= ((-1)(y-a)/(w+n)) * ((w+n)(w-n))/(y-a)\n\nThe (w+n)'s cancel out, as do the (y-a)'s, so you're left with this:\n\n= (-1)(w-n)\n= (n-w)
1029624
One big advantage is that rational exponents are easier to combine when more than one appears in an expression.\n\nI would say that something like the following would be easier to solve with rational exponents:\nThe square root of x to the 5th power, all divided by the cube root of x to the fourth power.\nWhen I see this equation, the way to simplify is to change the radicals to rational exponents--x to the 5/2 power divided by x to the 4/3 power--which can be further reduced by subtracting exponents.\n\nSince my first step in that problem is to change the radicals to rational exponents, that seems to "prove" (in some sense) that rational exponents are easier to work with in this type of problem.
390304
THE POSSIBILITIES:\n\n1.1:1→1*1=1\n2.1:2→1*2=2\n3.1:3→1*3=3\n4.1:4→1*4=4\n5.1:5→1*5=5 √\n6.1:6→1*6=6\n\n7.2:1→2*1=2\n8.2:2→2*2=2\n9.2:3→2*3=5\n10.2:4→2*4=8\n11.2:5→2*5=10 √\n12.2:6→2*6=12\n\n13.3:1→3*1=3\n14.3:2→3*2=6\n15.3:3→3*3=9\n16.3:4→3*4=12\n17.3:5→3*5=15 √\n18.3:6→3*6=18\n\n19.4:1→4*1=4\n20.4:2→4*2=8\n21.4:3→4*3=12\n22.4:4→4*4=16\n23.4:5→4*5=20 √\n24.4:6→4*6=24\n\n25.5:1→5*1=5    √\n26.5:2→5*2=10   √ \n27.5:3→5*3=15   √\n28.5:4→5*4=20   √\n29.5:5→5*5=25   √\n30.5:6→5*6=30   √\n\n31.6:1→6*1=6\n32.6:2→6*2=12\n33.6:3→6*3=18\n34.6:4→6*4=24\n35.6:5→6*5=30   √\n36.6:6→6*6=36\n\nProbability = No. of required possibilities/No. of total possible events =11/36\nSo the right answer is D
245176
u*(u-2)+v*(u-2)\n(u+v)*(u-2)
126171
No idea here too... what i know is that it could be simplified to 34x + 40. Dunno about the blank (____)
77913
Well, you need to know what the variable is equal to to solve. To simplify, if for example you had to devide -1 by x, you would write -1/x.\n\nBy the way, you don't have to start every question with "how in the world." Some more specifics would help though. If you are working on a specific problem, copy it word for word.
955805
That simplifies to 3[2x-1]>12\n\n[2x-1]>4\n\n2x-1>4    2x-1<-4\n\nx>5/2  or x<-3/2\n\nWhen you have absolute values, you have to look at both ends of the spectrum