we have
[tex]\sqrt{8x^{7}y^{8}}= ({8x^{7}y^{8}})^{\frac{1}{2}}=(2^{3})^{\frac{1}{2}} (x^{7})^{\frac{1}{2}} (y^{8})^{\frac{1}{2}}\\=(2x^{3}y^{4})(2x)^{\frac{1}{2}}=(2x^{3}y^{4})\sqrt{2x}[/tex]
therefore
the answer is the option
[tex](2x^{3}y^{4})\sqrt{2x}[/tex]
