Simplify the expression square root box (inside box: 18x^4y^3).
123815
First of all, you look like a nice girl and I do not like to see you/people teary eyed, so if you promise me you will try to be happier and not cry anymore, I will make an effort to teach you a whole bunch of nice lil' math tricks (explained in the simplest possible language that I can) to help you with your homework, ok? \n\nIn the problem at hand, first try and remember what a square root means, for example, something very simple like sqrt of 4 or simply sqrt(4).    Every time you get a square root problem like that you should ask yourself: what is that number which multiplied by itself will give me the number inside the square root (or inside the box as you put it) and the answer to that question will be the answer to the square root as well.  In case of 4 - a most simple example - the answer is obviously 2, since 2 multiplied by itself will equal 4 (i.e. the number under the square root).  In other words:  sqrt(4) = 2, because 2x2=4 simple as that.   The difficulty is, not every sqrt expression is as simple to immediately resolve as sqrt(4) for instance, especially when they involve variables, etc.   So, what should one do in more complex situations where the answer is not immediately obvious?   The solution is simple: You must learn and apply the rules of square roots and others like factoring, etc., to solve the problem; that's why we study mathematical rules to begin with.   Ok, back to the question at hand, namely sqrt(18x^4y^3).  Having done so many similar problems and having applied the rules to so many analogous exercises in my life, I know immediately in my head what the answer in this case is, and I promise you in time and with lots of practice you will be able to do the same.  However, since you are a beginner at this let's try to apply the rules and solve the problem step by step.   First of all, notice that everything under the sqrt is being multiplied by one another.   This makes our situation much easier to deal with since we can breakup that one big sqrt into smaller ones that you can more easily deal with:\nsqrt(18x^4y^3) = sqrt(18)sqrt(x^4)sqrt(y^3) = sqrt (2*9)sqrt(x^4)sqrt(y*y^2) = sqrt(2)sqrt(9)sqrt(x^4)sqrt(y)sqrt(y^2)\n\nNow notice in the above expression:\n\nsqrt(2) is as simplified as it can be\nsqrt(9) = 3   (since 3 * 3 = 9)\nsqrt(x^4) = x^2   (since x^2 * x^2 = x^4)\nsqrt(y) is as simplified as it can be\nand finally,\nsqrt(y^2) = y (since y*y = y^2)\n\nSo now substituting these values into the above expression we will have:\n\nsqrt(2)*3*x^2*sqrt(y)*y  ….and now with simple rearrangement of the terms and knowing that sqrt(2)sqrt(y) = sqrt(2y) we will finally have:\n\n3x^2*y*sqrt(2y)   which is the answer we are looking for.\n\n\nI hope that was helpful.    Good Luck and Practice, Practice, Practice!\n\nP.S.  Please take the time to read my response to one of the older questions I’ve answered entitled: “What’s the key to Understand Mathematics?” as well.    I am sure it will help you with some of your math challenges.
69467
2x-1(xsquared-x+10)squared
119382
3(16 y_squared - 24xy + 9 x_squared)
391845
If this is a problem in a math class, the answer provided by abcde12345 is correct. He shows you the technique to simplify it, which is to multiply numerator and denominator by the "conjugate" of the denominator (which just means you change the sign of the square root part, so you get (3 - sqrt(5)).\n\nIf this is a problem in physics or some other class, and all you need is a value, then follow the suggestion of some others who recommend using a calculator.
658266
The dist is\nsqrt.[(4-3)^2+(1-1)^2+(4-3)^2]=sqrt.2
456456
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
512625
4(-2)² + 8(-2) + 3(-2) + 6\n= 4(4) - 16 - 6 + 6\n= 16 - 16 + 6 - 6 = 0
429029
(17-9)**2+(9-18)**2\n\nthen square root of it will,  give u magnitude
381190
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
660632
18r^4s^5t^6\n---------------- =\n-3r^2st^3\n\n-6r^(4-2)s^(5-1)t^(6-3)= -6r^2s^4t^3\n\nhope it's not too late.\n\nGood luck!
360807
1. (xy^2)^3 (x^2y)^2 + (x^3y^4)(x^2y^2)^2\n(x^3y^6)(x^4y^2) + (x^3y^4)(x^4y^4)\nx^7y^8 + x^7y^8\n2x^7y^8\n\n2. (3x^2)(3y^2)+ 3x^2y - (3xy)^2 - 3xy^2\n9x^2y^2 + 3x^2y - 9x^2y^2 - 3xy^2\n9x^2y^2 - 9x^2y^2 + 3x^2y - 3xy^2\n3x^2y - 3xy^2\n\nSimplifying is fun.\n\nBarjesse37
584311
(3x-2)(12x^2-2) + (4x^3-x^2+1)(3)\n\nThat is the un-simplified answer
490591
2√72 + √32 - 4√18\n= 2(√8*√9) + (√8*√4) - 4 (√2*√9)\n= (2*3)√8 + 2√8 - (4*3)√2\n= 6(√2*√4) + 2(√2*√4) - 12√2\n= (6*2)√2 + (2*2)√2 - 12√2\n= 12√2 + 4√2 - 12√2\n= 4√2\n\nHope this helps.
286570
Adding radicals is impossible to simplify, unless the same radical, in which case it would be something like this...\nx√z + y√z = (x+y)√z\nOften times to do this you will need to simplify the root, doing so requires finding square divisors (ex. 4, 9, 16, ect.) Just divide the base of the root by that number (always has to be a square) then multiply the coeffecient of the root by the root of the number you divided out. \nExample:\n√24\nCan be divided by 4\n√6*4\nTake out the 4 and then multiply coeffecient (1 in this case) by the root of 4, 2\n2√6\n\nThat's about it...
394534
If you are allowed to head into the realm of complex/imaginary numbers, you could factor out a sqrt(-1) and replace it with a lowercase i.\n\nsqrt(-24) = sqrt(4) x sqrt(6) x sqrt(-1)\nsqrt(-24) = ± 2 sqrt(6) i
169546
Evaluation for it square root\n\nAs we know x^(y*2)=(x^y)^2\ntherefore 81^(1/4)=81^((1/2)*(1/2))=(81^1/2)^1/2\nhence 81^1/2=9\nand 9^1/2=3\nso answer is 3
53040
On top..\n4 plus or minus the square root of 8\non bottom..\nall over 4\n=(4 +or- sqrt8)/4\nIf you can find any factor of the number inside the radical sign which is a perfect square, then you may rewrite that number into the product of that perfect square and the 'other". Let's say 45. 9 is a factor of 45 and a perfect square, so 45 = 9 * 5.\nIn your given, 8 = 4 * 2. (4 is a perfect square) You may substitute this to the original equation:\n=(4 +or- sqrt(4*2))/4\nyou may then get the square root of that perfect square and place it out of the radical sign, leaving the 'other' number. Since 2 is the sqrt of 4, then\n=(4 +or- 2 (sqrt 2))/4\nThe numerator has a common monomial factor of 2 (One technique is to find if all terms are even). you can factor this out and use the cancellation method.\n=2(2 +or- sqrt 2)/4\nCancelling 2 from both numerator and denominator,\n=(2 +or- sqrt 2)/2\nYou have a +or- sign, so there are to answers:\n=(2 + sqrt 2)/2 or\n=(2 - sqrt 2)/2\nThese answers are accepted, but if you want, you can simplify sqrt 2 into 1.4142. So you will get:\n=1.7071 or\n=0.2929\nHope this helps ;-)