[tex]\displaystyle\bf\\\frac{2}{5}\sqrt{200} =\sqrt{\Big(\frac{2}{5}\Big)^{2} \cdot 200 }=\sqrt{\frac{4}{25} \cdot 200} =\sqrt{32} \\\\\\\frac{4}{5}\sqrt{50} =\sqrt{\Big(\frac{4}{5}\Big)^{2} \cdot 50 }=\sqrt{\frac{16}{25} \cdot 50} =\sqrt{32}\\\\\\\sqrt{32} =\sqrt{32} \ \ \ \Rightarrow \ \ \ \boxed{ \frac{2}{5} \sqrt{200}=\frac{4}{5} \sqrt{50} }[/tex]