Question 313178
Let's check. Let {{{x=y=1}}}.
{{{sqrt(1+1)=sqrt(1)+sqrt(1)}}}
{{{sqrt(2)=1+1}}}
{{{sqrt(2)=2}}}
No, that's not true.
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{{{sqrt(x+y)=sqrt(x)+sqrt(y)}}}
Square both sides.
{{{x+y=sqrt(x)sqrt(x)+sqrt(x)sqrt(y)+sqrt(y)sqrt(x)+sqrt(y)sqrt(y)}}}
{{{x+y=x+2sqrt(xy)+y)}}}
{{{2sqrt(xy)=0}}}
So the equation above only holds for certain values of x and y. 
It only holds when {{{x=0}}}, {{{y=0}}}, or {{{x=y=0}}}
Now you see why.