Simplify the expression:
[tex]3\sqrt{2y^3}\cdot7\sqrt{18y}[/tex]
Operate the coefficients and join the square roots:
[tex]3\cdot7\sqrt{2y^3\cdot18y}=21\sqrt{2y^3\cdot18y}[/tex]
Operate the radicand:
[tex]21\sqrt{36y^4}=21\sqrt{6^2(y^2)^2}[/tex]
The radicand now is a perfect square. Taking the square root:
[tex]21\cdot(6y^2)=126y^2[/tex][tex]\boxed{126y^2}[/tex]
