I'm going to assume the square root goes over everything.
To simplify this, you need to find perfect squares under the radical that are factors of the entire [tex]110x^{17}y^{12}[/tex].
[tex]\sqrt{110x^{17}y^{12}} = \sqrt{x^{16}y^{12}\cdot 110x^{1}}[/tex]
Now that stuff in the front will interact nicely with the square root, but the stuff in the back doesn't, so it just stays under the radical.
[tex]\sqrt{x^{16}y^{12}\cdot 110x^{1}} = \sqrt{x^{16}y^{12}}\cdot \sqrt{110x^{1}} =x^8y^6\cdot \sqrt{110x}[/tex]
And that end piece is the simplified answer.
