[tex]\frac{x^{3}y^{2}\sqrt{30y}}{5}[/tex].
In order to solve this problem we have to reduce the expression[tex]\frac{\sqrt{6x^{8}y^{9}}}{\sqrt{5x^{2}y^{4}}}[/tex].
First, we have to combine the expression in a single radical:
[tex]\sqrt{\frac{6x^{8}y^{9} }{5x^{2}y^{4}}}[/tex]
Second, we have to reduce the expression above by elimination of common factors:
[tex]\sqrt{\frac{x^{2}6x^{6}y^{4}y^{5} }{5x^{2}y^{4}}}\\\sqrt{\frac{6x^{6}y^{5} }{5}}[/tex]
rewriting the expression above:
[tex]\frac{\sqrt{6x^{6}y^{5}}}{\sqrt{5}}[/tex]
Simplifying:
[tex]\frac{\sqrt{(x^{3}y^{2})^{2}6y}}{\sqrt{5}}\\\frac{x^{3}y^{2}\sqrt{6y}}{\sqrt{5}}[/tex]
Multipliying the resultant expression by [tex]\frac{\sqrt{5}}{\sqrt{5}}[/tex]
[tex]\frac{x^{3}y^{2}\sqrt{6y}}{\sqrt{5}}\frac{\sqrt{5}}{\sqrt{5}}[/tex]
Resulting:
[tex]\frac{x^{3}y^{2}\sqrt{30y}}{5}[/tex]
