Odpowiedź:
[tex]\huge\boxed{NIE;\ 50\sqrt3\neq10\sqrt6}[/tex]
Szczegółowe wyjaśnienie:
Skorzystamy z:
[tex]b=\sqrt{b^2}\ \text{dla}\ b\geq0\\\\\sqrt{a}\cdot\sqrt{b}=\sqrt{a\cdot b}\ \text{dla}\ a\geq0\ \wedge\ b\geq0[/tex]
[tex]50\sqrt3=\sqrt{50^2}\cdot\sqrt3=\sqrt{2500}\cdot\sqrt3=\sqrt{2500\cdot3}=\sqrt{7500}[/tex]
[tex]10\sqrt6=\sqrt{10^2}\cdot\sqrt6=\sqrt{100}\cdot\sqrt6=\sqrt{100\cdot6}=\sqrt{600}[/tex]
[tex]\sqrt{7500}\neq\sqrt{600}\to50\sqrt3\neq10\sqrt6[/tex]
