Answer
$(2, \sqrt 2)$
Work Step by Step
$y= \sqrt x$
$x^2+y^2=6$
$x^2+y^2=6$
$x^2+(\sqrt x)^2=6$
$x^2+x=6$
$x^2+x-6=6-6$
$x^2+x-6=0$
$(x+3)(x-2)=0$
$x+3=0$
$x+3-3=0-3$
$x=-3$
This answer is not valid since we need to be able to take the square root of $x$.
$x-2=0$
$x-2+2=0+2$
$x=2$
$x^2+y^2=6$
$2^2+y^2=6$
$4+y^2=6$
$4+y^2-4=6-4$
$y^2=2$
$\sqrt {y^2}=\sqrt 2$
$y = \sqrt 2$
