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NotSoSmart  Jan 30, 2018

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\(\quad\,\frac{\sqrt3-\sqrt6}{\sqrt3+\sqrt6} \\~\\ =\,\frac{\sqrt3-\sqrt6}{\sqrt3+\sqrt6} \,\cdot\,\frac{\sqrt3-\sqrt6}{\sqrt3-\sqrt6}\\~\\ =\,\frac{3\,-\,2\sqrt{18}\,+\,6}{3\,-\,6} \\~\\ =\,\frac{9-2\sqrt{18}}{-3} \\~\\ =\,\frac{9-6\sqrt{2}}{-3} \\~\\ =\,-3+2\sqrt2\)

hectictar  Jan 30, 2018
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Best Answer

\(\quad\,\frac{\sqrt3-\sqrt6}{\sqrt3+\sqrt6} \\~\\ =\,\frac{\sqrt3-\sqrt6}{\sqrt3+\sqrt6} \,\cdot\,\frac{\sqrt3-\sqrt6}{\sqrt3-\sqrt6}\\~\\ =\,\frac{3\,-\,2\sqrt{18}\,+\,6}{3\,-\,6} \\~\\ =\,\frac{9-2\sqrt{18}}{-3} \\~\\ =\,\frac{9-6\sqrt{2}}{-3} \\~\\ =\,-3+2\sqrt2\)

hectictar  Jan 30, 2018

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