Elementary Algebra

$y=34/9$
Recall, in order to cancel out a square root, we square both sides of the equation. Thus, we square both sides of the equation to obtain that 9(y-2)=16. We now simplify: $9y-18=16 \\\\ 9y=34 \\\\ y=34/9$ We now must check our solution: $3\sqrt{34/9-2}=4 \\\\ 3\sqrt{16/9} =4 \\\\ 3(4/3) =4 \\\\ 4=4$ This is true, so our solution is valid.