Question

simplify: 1/ ( root3 + root2 - root5)

Answer 1

Answer:

$\frac{1}{\sqrt{3}+\sqrt{2}-\sqrt{5}}=\frac{3\sqrt{2}+2\sqrt{3}+\sqrt{30}}{12}$

Step-by-step explanation:

$Given \: \frac{1}{\sqrt{3}+\sqrt{2}-\sqrt{5}}$

$=\frac{\sqrt{3}+\sqrt{2}+\sqrt{5}}{(\sqrt{3}+\sqrt{2}-\sqrt{5})(\sqrt{3}+\sqrt{2}+\sqrt{5})}$

$=\frac{\sqrt{3}+\sqrt{2}+\sqrt{5}}{(\sqrt{3}+\sqrt{2})^{2}-(\sqrt{5})^{2}}$

$=\frac{\sqrt{3}+\sqrt{2}+\sqrt{5}}{3+2+2\sqrt{6}-5}$

$=\frac{\sqrt{3}+\sqrt{2}+\sqrt{5}}{5+2\sqrt{6}-5}$

$=\frac{\sqrt{3}+\sqrt{2}+\sqrt{5}}{2\sqrt{6}}$

$=\frac{\sqrt{6}(\sqrt{3}+\sqrt{2}+\sqrt{5})}{2\sqrt{6}\times \sqrt{6}}$

$=\frac{3\sqrt{2}+2\sqrt{3}+\sqrt{30}}{12}$

Therefore,

$\frac{1}{\sqrt{3}+\sqrt{2}-\sqrt{5}}=\frac{3\sqrt{2}+2\sqrt{3}+\sqrt{30}}{12}$

•••♪

Answer 2

Answer:

1 / √3+√2-√5

:-

√30+3√2+2√3 / 12

thank u