Solution:
Given:
[tex]\sqrt{18x^7y^6}[/tex]
Splitting the expressions further to get the perfect squares out:
[tex]\begin{gathered} \sqrt{18x^7y^6}=\sqrt{9\times2\times(x^6\cdot x)\times(y^3)^2} \\ =\sqrt{9\times2\times(x^3)^2\cdot x\times(y^3)^2} \end{gathered}[/tex]
[tex]\begin{gathered} \sqrt{18x^7y^6}=\sqrt{9\times2\times(x^3)^2\cdot x\times(y^3)^2} \\ =3x^3y^3\sqrt{2x} \end{gathered}[/tex]
Therefore, the correct answer is:
[tex]3x^3y^3\sqrt{2x}[/tex]
