$$\frac{\sqrt{2}+\sqrt{5}}{2+\sqrt{10}}$$
$\frac{\sqrt{2}}{2}\approx 0.707106781$
$$\frac{\left(\sqrt{2}+\sqrt{5}\right)\left(2-\sqrt{10}\right)}{\left(2+\sqrt{10}\right)\left(2-\sqrt{10}\right)}$$
$$\frac{\left(\sqrt{2}+\sqrt{5}\right)\left(2-\sqrt{10}\right)}{2^{2}-\left(\sqrt{10}\right)^{2}}$$
$$\frac{\left(\sqrt{2}+\sqrt{5}\right)\left(2-\sqrt{10}\right)}{4-10}$$
$$\frac{\left(\sqrt{2}+\sqrt{5}\right)\left(2-\sqrt{10}\right)}{-6}$$
$$\frac{2\sqrt{2}-\sqrt{2}\sqrt{10}+2\sqrt{5}-\sqrt{5}\sqrt{10}}{-6}$$
$$\frac{2\sqrt{2}-\sqrt{2}\sqrt{2}\sqrt{5}+2\sqrt{5}-\sqrt{5}\sqrt{10}}{-6}$$
$$\frac{2\sqrt{2}-2\sqrt{5}+2\sqrt{5}-\sqrt{5}\sqrt{10}}{-6}$$
$$\frac{2\sqrt{2}-\sqrt{5}\sqrt{10}}{-6}$$
$$\frac{2\sqrt{2}-\sqrt{5}\sqrt{5}\sqrt{2}}{-6}$$
$$\frac{2\sqrt{2}-5\sqrt{2}}{-6}$$
$$\frac{-3\sqrt{2}}{-6}$$
$$\frac{1}{2}\sqrt{2}$$
Show Solution
Hide Solution
