Question

Help really quick?

Answer 1

Im thinking its B.. or D.. Im not sure.

Answer 2

@satellite73

Answer 3

@mathmale

Answer 4

Multiply top and bottom by the conjugate

\[\large \frac{\sqrt{2} - \sqrt{10}}{\sqrt{2} + \sqrt{10}} \times \frac{\sqrt{2} - \sqrt{10}}{\sqrt{2} - \sqrt{10}}\]

Which simplifies to

\[\large \frac{(\sqrt{2} - \sqrt{10})(\sqrt{2} - \sqrt{10})}{(\sqrt{2} + \sqrt{10})(\sqrt{2} - \sqrt{10})}\]
or
\[\large \frac{2 - 4\sqrt{5}+ 10}{2 - 10}\]
\[\large -\frac{12 - 4\sqrt{5}}{8}\]
\[\large -\frac{12}{8} + \frac{4\sqrt{5}}{8}\]

So I get

\[\large -\frac{3}{2} + \frac{1}{2}\sqrt{5}\]