[tex]\sqrt{64x^6}\\\\Use\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\=\sqrt{64}\cdot\sqrt{x^6}=8\sqrt{x^6}\\\\Use\ (a^n)^m=a^{nm}\\\\=8\sqrt{x^{3\cdot2}}=8\sqrt{(x^3)^2}\\\\Use\ \sqrt{a^2}=|a|\\\\=\boxed{8|x^3|=8|x|^3}\to\boxed{C.}[/tex]
