Question 51968
{{{x-sqrt(x)=0}}}  can be solved algebraically a couple of different ways.  I showed another student one way to solve it earlier today.  Look it up and I'll show you a second way to do it.
{{{x-sqrt(x)=0}}} 
{{{x-sqrt(x)+sqrt(x)=0+sqrt(x)}}} (add {{{sqrt(x)}}} to both sides)
{{{x=sqrt(x)}}}   (simplify)
{{{(x)^2=(sqrt(x))^2}}}  (square both sides)
{{{x^2=x}}}
{{{x^2-x=x-x}}}   (subtract x from both sides)
{{{x(x-1)=0}}}     (factor out an x)
x=0 and x-1=0 (zero product property)
x=0 and x-1+1=0+1 
x=0 and x=1
Because this involves a square root you'll need to check for false solutions called extraneous solutions by substituting the answers back into the original equations to make sure they work.
{{{(0)-sqrt(0)=0}}}
0-0=0 
{{{(1)-sqrt(1)=0}}}
1-1=0
Both x=0 and x=1 are valid solutions.
As for the graphing:
y=x is a line, you can substitute values for x and get coordinates for points to connect.
When x=0, y=0 gives you the coordinate  (0,0)
When x =1, y=1   (1,1)
When x=2, y=2    (2,2)
For {{{y=sqrt(x)}}}
When x=0, {{{y=sqrt(0)}}}
          y=0    (0,0)
When x=1, {{{y=sqrt(1)}}}
          y=1    (1,1)
When x=4, {{{y=sqrt(4)}}}
          y=2    (4,2)

When you plot all those points, you'll see that the two graphs intersect at x=0 and x=1.  This verifies our algebraic answer.
{{{graph(300,200,-1,6,-1,4,x,sqrt(x))}}}
Happy Calculating!!!