[tex]7\sqrt{50x^{15}y^{21}}=7\sqrt{25\cdot2x^{14+1}y^{20+1}}=7\sqrt{25}\cdot\sqrt{x^{14}}\cdot\sqrt{y^{20}}\cdot\sqrt{2xy}\\\\=7(5)\sqrt{(x^7)^2}\cdot\sqrt{(y^{10})^2}\cdot\sqrt{2xy}=35x^7y^{10}\sqrt{2xy}\\\\Used:\\\\\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\\sqrt{a^2}=a\\\\a^n\cdot a^m=a^{nm}\\\\(a^n)^m=a^{nm}[/tex]
