Question 198817
Let's say that you want to find the distance between two points. You will then use that distance and add it to other distances you find. Also, you want to keep your calculations as exact as possible (to avoid any errors). To keep things exact, you most likely end up with a radical.


For example, let's say that you want to find the distance between the points (1,2) and (5,8):


{{{d=sqrt((x[1]-x[2])^2+(y[1]-y[2])^2)}}} Start with the distance formula.



{{{d=sqrt((1-5)^2+(2-8)^2)}}} Plug in {{{x[1]=1}}},  {{{x[2]=5}}}, {{{y[1]=2}}}, and {{{y[2]=8}}}.



{{{d=sqrt((-4)^2+(2-8)^2)}}} Subtract {{{5}}} from {{{1}}} to get {{{-4}}}.



{{{d=sqrt((-4)^2+(-6)^2)}}} Subtract {{{8}}} from {{{2}}} to get {{{-6}}}.



{{{d=sqrt(16+(-6)^2)}}} Square {{{-4}}} to get {{{16}}}.



{{{d=sqrt(16+36)}}} Square {{{-6}}} to get {{{36}}}.



{{{d=sqrt(52)}}} Add {{{16}}} to {{{36}}} to get {{{52}}}.



{{{d=2*sqrt(13)}}} Simplify the square root.



Now if you found other distances (in terms of radicals), you could add them to this given distance and keep things exact. Once you are done with all of your calculations, you can use a calculator to find the approximate value.