Answer:
[tex]\large\boxed{\sqrt{90x^5}=3x^2\sqrt{10x}}[/tex]
Step-by-step explanation:
[tex]Domain:\ x\geq0\\\\\sqrt{90x^5}=\sqrt{9\cdot10\cdot x^{2+2+1}}\\\\\text{use}\ a^n\cdot a^m=a^{n+m}\\\\=\sqrt{9\cdot10\cdot x^2\cdot x^2\cdot x^1}\\\\\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\=\sqrt9\cdot\sqrt{10}\cdot\sqrt{x^2}\cdot\sqrt{x^2}\cdot\sqrt{x}\\\\\text{use}\ \sqrt{a^2}=a\ \text{for}\ a\geq0\\\\=3\cdot\sqrt{10}\cdot x\cdot x\cdot\sqrt{x}=3x^2\sqrt{10x}[/tex]
