Answer
$y=41/16$
Work Step by Step
$\sqrt {y+5} = 2+\sqrt{y-2}$
$(\sqrt {y+5})^2 = (2+\sqrt{y-2})^2$
$y+5=2*2+2(\sqrt{y-2})+2(\sqrt{y-2})+\sqrt{y-2}*\sqrt{y-2}$
$y+5=4+4\sqrt{y-2}+(y-2)$
$y+5=4+4\sqrt{y-2}+y-2$
$y+5=y+2+4\sqrt{y-2}$
$3=4\sqrt{y-2}$
$3/4=4\sqrt{y-2}/4$
$3/4=\sqrt{y-2}$
$(3/4)^2=(\sqrt{y-2})^2$
$9/16=y-2$
$9/16+2=y$
$41/16=y$
$\sqrt {y+5} = 2+\sqrt{y-2}$
$\sqrt {41/16+5} = 2+\sqrt{41/16-2}$
$\sqrt {121/16} = 2+\sqrt{9/16}$
$11/4=2+3/4$
$11/4=8/4+3/4$
$11/4=11/4$ (true)
