$\sqrt{18x^{12}}=\sqrt{9\ast <!--\; \ast \; -->2\ast <!--\; \ast \; -->(x^6{)}^2}=\sqrt{9}\ast <!--\; \ast \; -->\sqrt{2}\ast <!--\; \ast \; -->\sqrt{(x^6{)}^2}=3\sqrt{2}{x}^6$

$\sqrt{y^9}=\sqrt{y^8\ast <!--\; \ast \; -->y}=\sqrt{(y^4{)}^2\ast <!--\; \ast \; -->y}=\sqrt{(y^4{)}^2}\ast <!--\; \ast \; -->\sqrt{y}=y^4\sqrt{y}$