Question 843034
Isolate r and any expressions with it onto one side; usually the simplest.


{{{160 = Pi *r* Sqrt(36 + r^2)}}}
{{{160/pi=r*sqrt(36+r^2)}}}
{{{(160/pi)^2=r^2(36+r^2)}}}
{{{36r^2+r^4=(160/pi)^2}}}
{{{r^4+36r^2-(160/pi)^2=0}}} ----- this is in quadratic form, and you need to first solve for {{{r^2}}}.


Let {{{u=r^2}}}
Let {{{d=discriminant=36^2+4(160/pi)^2=highlight_green(1296+102400/(pi^2))}}}
{{{u^2+36u-(160/pi)^2}}}
-
{{{highlight(u=(-36+- sqrt(1296+102400/(pi^2)))/(2))}}} ----which part way to the answer.
{{{r=sqrt(u)=highlight(0+- sqrt((-36+- sqrt(1296+102400/pi))/(2)))}}}
which you still want to try to simplify.