How do you simplify $\frac{\sqrt{22}}{\sqrt{11} - \sqrt{66}}$ $sqrt22/(sqrt11-sqrt66)$ ?

Question

1866 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-11-01T14:04:22

Use $\sqrt{a b} = \sqrt{a} \sqrt{b}$ $sqrt(ab) = sqrt(a)sqrt(b)$ to find:

$\frac{\sqrt{22}}{\sqrt{11} - \sqrt{66}} = - \frac{\sqrt{2}}{5} - \frac{2 \sqrt{3}}{5}$ $sqrt(22)/(sqrt(11)-sqrt(66))=-sqrt(2)/5-(2sqrt(3))/5$

If $a, b \geq 0$ $a, b >= 0$ then $\sqrt{a b} = \sqrt{a} \sqrt{b}$ $sqrt(ab) = sqrt(a)sqrt(b)$

So:

$\frac{\sqrt{22}}{\sqrt{11} - \sqrt{66}}$ $sqrt(22)/(sqrt(11)-sqrt(66))$

$= \frac{\sqrt{11} \sqrt{2}}{\sqrt{11} - \sqrt{11} \sqrt{6}}$ $=(sqrt(11)sqrt(2))/(sqrt(11)-sqrt(11)sqrt(6))$

$= \frac{\sqrt{2}}{1 - \sqrt{6}}$ $=sqrt(2)/(1-sqrt(6))$

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

$= \frac{\sqrt{2} + {\sqrt{2}}^{2} \sqrt{3}}{1 - 6}$ $=(sqrt(2)+sqrt(2)^2sqrt(3))/(1-6)$

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

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

How do you simplify √22√11−√66sqrt22/(sqrt11-sqrt66)?