HELP! Divide, rationalize the denomnator if necessary, then simplify the radical expression: (sqrt54n^5)/sqrt3
960500
√(54n^5) = √(9*6*n^4*n) = 3n² √6n\n\nSo √(54n^5) / √3 = \n\n3n² √6n / √3\n\nBut √6 / √3 = √2\n\nSo 3n² √6n / √3 = \n\n3n² √2n\n\nNRT
762368
NB! sqrt(x)=x^½ \n2*(2+1)^½ / -5*(2+3)^½<=>\n( 2*(3)^½*(5)^½ )/(-5*5)<=>\n( -2*(3*5)^½ )/25<=>\n( -2(15)^½ )/25<=>\n-2( 3*5/5*5*5*5)^½<=>\n-2(3/5*5*5)^½= -sqrt(3/5)*2/5\n=========================
511277
rationalising both numerator nd denominator by the conjugate of the denomenator.\n  2+i/1-3i  mutiplied by 1+3i/1+3i\n =(2+i)(1+3i)/(1-3i)(1+3i)\n =2+6i+i+3(-1)/1-3(-1)\n =2+7i-3/1+3\n =7i-1/4\n =7i/4-1/4......is ur answer.
923840
Here's how I would do it:\n\nTo remove the sqrt, you square both sides:\n\nsqrt(p^2 - 3p + 16) = (p+1)(p+1)\np^2 - 3p + 16 = p^2 + 2p + 1\n\nThen it's basic algebra. The p^2 are out of there, and you are left with\n\n-3p + 16 = 2p + 1\n16-1=2p+3p\n15=5p\np=3\n\nSo, let's check:\nsqrt(3^2 - 3(3) + 16) = 3+1\nsqrt(9-9+16)=4\nsqrt 16 =4\n\nThe person who put -5 as one of the answers... it doesn't work:\n\nsqrt ((-5)^2 -3(-5) + 16) = -5+1\nsqrt (25+15+16)= -4\nsqrt 56= -4 This is false, so -5 is not an answer.
1090065
Multiply the numerator and denominator by (√ x + ∆x ) + ( √ x ) \n[(√ x + ∆x ) - ( √ x )][( √ x + ∆x ) + ( √ x )]\n= x + ∆x - x \n= ∆x\n∆x/[∆x[(√ x + ∆x ) + ( √ x )]]\n= 1/[(√ x + ∆x ) + ( √ x )]\nReplace ∆x with 0.\n= 1/[(√ x + 0 ) + ( √ x )]\n= 1/[(√ x ) + ( √ x )]\n= 1/(2√ x )
774933
if the numbers are both under a radical...divide the numbers...put answer under radical...if perfect square or contain a perfect square... simplify\nsqrt(4)/sqrt(2) = sqrt (4/2) =sqrt 2\nsqrt(36)/sqrt(9) = sqrt(36/9)=sqrt 4 =2
354088
sqrt(75a^2) can be written as\n\nsqrt(15) * sqrt(5) * sqrt(a^2)\n\nSo cancel out the sqrt(5) in the numerator and denominator, take the square root of a^2, and you have\n\na * sqrt(15)\n\nThis cannot be simplified further.
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.
555590
Just multiply:\n(X/3)(3/4 x) -(x/3)(3/5) + (3/4)(3/4x) - (3/4)(3/5)\n\nand simplify from there
790653
In order to solve, you need a common denominator:\n2(sqrt(3/5)) - 5(sqrt (5/3))\n2(sqrt 3/sqrt 5) - 5 (sqrt 5/sqrt 3)\n2(sqrt3/sqrt3)(sqrt 3/sqrt 5) - 5(sqrt 5/sqrt 5)(sqrt 5/sqrt 3)\n2(3/sqrt 15) - 5(5/sqrt 15)\n6/sqrt 15 - 25/sqrt 15\n-19/sqrt 15
802282
(n + 3)(2n + 3) = (n + 2)^2 + (n 2)2^2\nFirst use FOIL to simplify\n2n^2 + 3n + 6n + 9 = n^2 + 2n + 2n + 4 + n^4\nCombine like terms on each side\n2n^2 + 9n + 9 = n^4 + n^2 + 4n + 4\nMove everything over to one side.\nn^4 - n^2 - 5n - 5 = 0\nFactor.\n(x+1)(x^3 -x^2 -5) = 0\nThat means x+1 = 0 or x^3 -x^2 -5 = 0\nx+1 = 0 when x = -1\nx^3 -x^2 -5 = 0 when  = 2.1163
238375
I'd start by pairing them up a bit to simplify common denominators.\n0/1 = 0\n1/2+3/4+7/8 = 4/8+6/8+7/8 = 17/8\n2/3+5/6+8/9 = 12/18+15/18+16/18 = 43/18\n4/5+6/7 = 28/35+30/35 = 58/35\n\nNow there's only 3 fractions, 58/35+43/18+17/8.  Time to find the grand common denominator.  I'm using underscores to indent since spaces get stripped out.\n_35\nx18\n- - -\n280\n35\n- - -\n630\n\n_630\nx__8\n- - - -\n5040\n\nBut since 2 will go into 630 and 8, we can reduce that by half, 2520.\nNow, find the multipliers we want through long division to use against the numerators.\n\n_____72\n35 | 2520\n___245\n___- - -\n____070\n_____70\n_____- -\n______0\n\n\n____140\n18 | 2520\n___18\n___- -\n___072\n____72\n____- -\n____000...\n\nThis is too tedious after all.  Guess I'll keep going, but I'm going to use my calculator a little, now.\n\n2520/35=72\n2520/18=140\n2520/8=315\n\n58/35+43/18+17/8 =\n4176/2520+6020/2520+5355/2520 =\n15551/2520\n\nAnd that's my final answer.  What do I win?
514501
It's not really a problem as much as a simplification; there's no = sign.  Anyway, simplified I get 8w^3 + 4w^2.  I got that by multiplying your original problem by \n(-2w-1)/(-2w-1).  That gets rid of the fraction in the denominator and reduces the numerals in the numerator down.
167162
I do agree with Anniemc46.\nIf the denominator is 1+(tanhx)^2 then it is easy to do.\n\nI have done and uploaded to my web site.\nPlease check the url I provided in the sourse.\n\nThanking U,\nThuvalpakshi.
934867
(√3x²z³) * (√15x²z )\n\n(√3x²z) (√z²)  * (√3x²z) (√5z)\n\n3x²z (√5z³ )\n   \n3(√5) x²z²  <--answer\n\nor\n\n√3x²z³ * √15x²z \n\n(√45x^4z^4)\n\n(√[9*5]x^4z^4)\n\n3(√5)x²z²  <--answer
980606
If you have to simplify then you have to get the denominator common. So,\n\nThe numerator of the equation is: \n\n{ [ 3 x (2c^2 + c) x (6c) ] - [ (c - 4) x (4c +2) x (6c) ] - [ 5 x (4c +2) x (2c^2 + c) ] }\n\nThis whole equation that the numerator above is then divided by the denominator which is as below\n\n[ (4c + 2) x (2c^2 + c) x (6c) ]\n\nI hope you will know where you are wrong now.
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