Question 73038
{{{x-sqrt(x)=0}}}Add {{{sqrt(x)}}} to both sides
{{{x^2=(sqrt(x))^2}}}}Square both sides
{{{x^2=x}}}Subtract from sides
{{{x^2-x=0}}}
{{{x(x-1)=0}}}Factor out an x
{{{x=0}}}One solution
{{{x-1=0}}}
{{{x=1}}}
The graph of {{{x-sqrt(x)=0}}} represents the x intercepts. In a sense, y=0 which allows you to find the x-intercepts.
{{{graph( 300, 200, -5, 5, -2, 2, x-sqrt(x))}}}Notice the x-intercepts at x=0 and x=1 (it may be hard to see the x=0 solution)
Hope this helps.