Answer:
[tex]\large\boxed{\sqrt{8x^7}=2x^3\sqrt{2x}}[/tex]
Step-by-step explanation:
[tex]Domain:\ x\geq0\\\\\sqrt{8x^7}=\sqrt{4\cdot2\cdot x^{2+2+2+1}}\\\\\text{use}\ a^n\cdot a^m=a^{n+m}\\\\=\sqrt{4\cdot2\cdot x^2\cdot x^2\cdot x^2\cdot x^1}\\\\\text{use}\ \sqrt{a\cdot b}=\sqrt{a}\cdot\sqrt{b}\\\\=\sqrt4\cdot\sqrt2\cdot\sqrt{x^2}\cdot\sqrt{x^2}\cdot\sqrt{x^2}\cdot\sqrt{x}\\\\\text{use}\ \sqrt{a^2}=a\ \text{for}\ a\geq0\\\\=2\cdot\sqrt2\cdot x\cdot x\cdot x\cdot\sqrt{x}=2x^3\sqrt{2x}[/tex]
