Answer:
[tex]\large\boxed{5x^2y^3\sqrt{5y}}[/tex]
Step-by-step explanation:
[tex]\sqrt{125x^4y^7}=\sqrt{25\cdot5\cdot x^{2+2}\cdot y^{2+2+2+1}}\\\\\text{use}\ a^n\cdot a^m=a^{n+m}}\\\\=\sqrt{25\cdot5\cdot x^2\cdot x^2\cdot y^2\cdot y^2\cdot y^2\cdot y^1}\\\\\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\=\sqrt{25}\cdot\sqrt5\cdot\sqrt{x^2}\cdot\sqrt{x^2}\cdot\sqrt{y^2}\cdot\sqrt{y^2}\cdot\sqrt{y^2}\cdot\sqrt{y}\\\\\text{use}\ \sqrt{a^2}=a\ \text{for}\ a\geq0\\\\=5\cdot\sqrt5\cdot x\cdot x\cdot y\cdot y\cdot y\cdot\sqrt{y}\\\\=5x^2y^3\sqrt{5y}[/tex]
