Question 36576
The basic strategy in solving a radical equation is to isolate the radical.  {{{x - 2*sqrt(x) = 0}}}.  


You can do this by adding {{{+2* sqrt(x) }}} to each side:

{{{x= 2* sqrt(x)}}}


Now, square both sides:

{{{x^2 = (2*sqrt(x))^2}}}
{{{x^2 = 4* x}}}


This is a quadratic equation, so set it equal to zero by subtracting 4x from each side:
{{{x^2 - 4x= 0}}}

{{{x(x-4) = 0}}}
x=0 or x = 4


Check for extraneous solutions.  Make sure these answers check!!

x=0
{{{x= 2* sqrt(x)}}}
{{{0= 2* sqrt(0) }}}
{{{0=2*0}}} It checks!


x= 4
{{{x= 2* sqrt(x) }}}
{{{4= 2* sqrt(4) }}}  It checks!


Now graph {{{y = x}}} and {{{y = 2*sqrt(x)}}}, and  find the points of intersection:


{{{ graph (300, 300, -6,6, -6,6, x, 2*sqrt(x) )}}}

Notice how the graphs cross at x = 0 and at x = 4.


R^2 at SCC