Question

Racionalize √5-√2/√5+✓2​

Answer 1

   $\frac{\sqrt{5}-\sqrt{2}}{\sqrt{5}+\sqrt{2}}=$

$=\frac{(\sqrt{5}-\sqrt{2})^{2}}{(\sqrt{5}+\sqrt{2})(\sqrt{5}-\sqrt{2})}=$

$=\frac{(\sqrt{5})^{2}-2\sqrt{5}\sqrt{2}+(\sqrt{2})^{2}}{(\sqrt{5})^{2}-(\sqrt{2})^{2}}=$

$=\frac{5-2\sqrt{10}+2}{5-2}=$

$=\frac{7-2\sqrt{10}}{3}$