How do you simplify the sqrt(10 - 2*sqrt(21)) to remove the inner radical?
460242
ur answer is [sqrt(3) - sqrt(7)].it can written as sqrt[x +/- 2*sqrt[y]] when x=a^2 + b^2 and y=a*b is equal to sqrt(a) +/- sqrt(b)
606423
Here's how to work it out:\n\n(Sorry, because I can't use special symbols, I'm using _/ for the square root symbol and <= for the less than or equal to symbol.)\n\n_/3x + 6 + 4 <= 7\n_/3x + 10 <= 7\n3x + 10 <= 7 x 7\n3x + 10 <= 49\n3x + 10 - 10 <= 49 - 10\n3x <= 39\n3x/3 <= 39/3\nx <= 13
346405
You have to solve the equation so that you can eliminate the sqrt by raising it to the second power .for instance,\n\nsqrt(2x+10)=5     you square it and get\n\n2x+10=25   easy, isnt it?\n\nbe careful if you have something like this\n\nsqrt(x+3)+sqrt(x-2)= 5\n\nhere you cannot do that you have to distribute one sqrt on each side of the equation.\n\nsqrt(x+3)=5-sqrt(x-2)\n\nnow you can square them
879678
The first thing to do is to find the factors of the number you're taking the root of.\nFor example, teh factors of 24 include 2*12, 3*8, and 4*6.\nSince four is a perfect square (2^2), we'll use that set of factors.\nSo:\nsqrt(24)= sqrt(4*6)= sqrt(4)*sqrt(6)= 2sqrt(6)\n\nSame with sqrt(18):\n18=9*2\n9=3^2\nsqrt(18)= sqrt(9)*sqrt(2)= 3sqrt(2)\n\nsqrt(3) +sqrt(3) can only be reduced by realizing that it's\n2*sqrt(3), which could be the sqrt(12). THis is because you can take the two under the radical by squaring it. so  you get sqrt (2^2+3)= sqrt(12), but technically 2sqrt(3) is more reduced.\n\nsqrt(27)=3 sqrt(3)\nsqrt(12)= 2 sqrt(3)\nso 3sqrt(3) + 2sqrt(3) = 5sqrt(3)\nin this case, you're treating the sqrt(3) sort of like it was a variable. think of 3x +2x = 5x
382118
(10^2-10^2)/10(10-10)\n= (10+10)10-10)/10(10-10)\n= 20/10 = 2
1149797
The first one is (-5, 3). I don't remember how to do the others.
782506
(  4 * (2)^(1/2)    ,    45 degrees)\n\n\n(   - 4 * (2)^(1/2)   , 225 degrees)\n\n\n\nand that big jumble on the start of each is 4 times the square root of 2, or the square root of 32, AKA (32)^(1/2). Math is hard on keyboards.
1122465
Just plug in 1 for x.\n√(1-1) = √0 = 0
308931
sqrt(160) = sqrt(16*10) = sqrt(16)*sqrt(10) = 4 sqrt(10) ~ 12.6491
204269
isolate one of the radicals, then square both sides.\nhere you get 2x+3=5x-6.......3x=9.......x=3\n\nworst case is sqrt(something) + something = sqrt(something)\n\nhere you'd isolate a radical, square both sides, clean up the equation, isolate the remaining radical, square both sides, and finish.  AND CHECK YOUR ANSWERS.  when you square both sides, "extraneous" solutions sneak in that might have you, back in the original equation, taking the square root of something negative.\n\nexample:  sqrt(3x+3) + 1 = sqrt(5x+6)\n....... (3x+3)+2*sqrt(3x+3)+1=(5x+6) ..... left side is a binomial\n.........2*sqrt(3x+3) = 2x+2\n...........sqrt(3x+3) = x+1\n...............(3x+3) = x^2+2x+1 ....... right side is a binomial\n....................0 = x^2-x-2 ......... and it factors!\n....................0 = (x-2)(x+1)\n....................0 = (x-2) so x=2\nor .................0 = (x+1) so x=-1\n\nnow check: sqrt(3*2+3)+1 =? sqrt(5*2+6)\n.............sqrt(9) + 1 =? sqrt(16)\n...................3 + 1 = 4.............yes.\n\n..........sqrt(3*-1+3)+1 = sqrt(5*-1+6)\n...............sqrt(0)+1 = sqrt(1)\n.......................1 = 1 ............yes\n\nsigh.  when I wrote it the equal signs lined up.
767712
First you find the square root of both the numerator and the denominator which would end up being √5/√8. This would be a fine answer, but in my math classes teachers have had rules against keeping a radical in the denominator. so, to get rid of that multiply √5/√8 by √8/√8, which gives you √40/√64, or √40/8.
983612
First swap the variables, then solve for R again.\n\nv = (21/2) - (1/64)R^2\nR^2 = -64v + 672\nR = ±√(-64v + 672)
458909
You can goto http://www.math.com 's square root calculator and figure out that it is about 20.78 so since an integer is a decimal-less number the answer would be between 20 and 21.\n\nShort of using the sqrt function of a calculator if you know that 20 squared is 400 and that is close to 43 you might then try squaring 21 and get 441 then realize 432's sqrt must be between 20 and 21.
282417
radical is sqrt? i think\n\n10 sqrt(20) / sqrt(64)=\n10 sqrt(4*5) / 8 =\n10 * 2 * sqrt (5) /8 = \n20 * sqrt (5) / 8 =\n5 sqrt(5) /2=\n2.5 radical 5
752173
Sqrt(3x/2) = Sqrt(3x/2) * SQRT(2/2) = SQRT(6x/4) = 1/2 * SQRT(6x)\n\n6*SQRT(7) - SQR(28) = 6*SQRT(7) - SQR(4*7) = 6*SQRT(7) - 2*SQR(7) = 4 * SQRT(7)
465898
sqrt(20/3)\n(sqrt(20))/(sqrt(3))\nMultiply top and bottom by sqrt(3)\n(sqrt(60))/3\n(sqrt(4 * 15))/3\n(2sqrt(15))/3
675662
Step 1:  Isolate the radical term.\nSqrt(5x)=x-4\n\nStep 2:  Square both sides.\n5x=(x-4)^2\n\nStep 3:  Expand, and combine like terms.\n5x=x^2-8x+16\nx^2-13x+16=0\n\nStep 4:  Use the quadratic formula.\nx=[-b+/-Sqrt(b^2-4ac)]/2a\n=[13+/-Sqrt(169-64)]/2\n=(13+Sqrt105)/2 and (13-Sqrt105)/2 which is approx.\n=11.6235 and 1.3765\n\nStep 5:  Check the answers.\nThe first one works in the original equation.\nThe second one does not.  It is an extraneous solution.\n\nThe only solution is (13+Sqrt105)/2.\n\nNOTE:  Purdue Engineer was close, but he was mistaken about which answer is extraneous.