How do you simplify $\frac{1 - \sqrt{2}}{2 + \sqrt{6}}$ $(1-sqrt2)/(2+sqrt6)$ ?

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How do you simplify $\frac{1 - \sqrt{2}}{2 + \sqrt{6}}$ $(1-sqrt2)/(2+sqrt6)$ ?

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Answer 1 · 2018-04-10T21:24:52

$= \frac{2 - 3 \sqrt{6} + 2 \sqrt{3}}{- 2}$ $=(2-3sqrt(6)+2sqrt(3))/(-2)$

Explanation:

Rationalise :

$\frac{1 - \sqrt{2}}{2 + \sqrt{6}}$ $(1-sqrt(2))/(2+sqrt(6))$ $\times$ $xx$ $\frac{2 - \sqrt{6}}{2 - \sqrt{6}}$ $(2-sqrt(6))/(2-sqrt(6))$

$\Rightarrow$ $=>$ $= \frac{2 - \sqrt{6} - 2 \sqrt{6} + \sqrt{12}}{4 - 2 \sqrt{6} + 2 \sqrt{6} - 6}$ $=(2-sqrt(6)-2sqrt(6)+sqrt(12))/(4-2sqrt(6)+2sqrt(6)-6$

$\Rightarrow$ $=>$ . $= \frac{2 - 3 \sqrt{6} + 2 \sqrt{3}}{- 2}$ $=(2-3sqrt(6)+2sqrt(3))/(-2)$

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How do you simplify $\frac{1 - \sqrt{2}}{2 + \sqrt{6}}$ $(1-sqrt2)/(2+sqrt6)$ ?

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