How do you simplify $sqrt22/(sqrt11-sqrt66)$ ?

Question

1868 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-11-01T14:04:22

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

$sqrt(22)/(sqrt(11)-sqrt(66))=-sqrt(2)/5-(2sqrt(3))/5$

If $a, b >= 0$ then $sqrt(ab) = sqrt(a)sqrt(b)$

So:

$sqrt(22)/(sqrt(11)-sqrt(66))$

$=(sqrt(11)sqrt(2))/(sqrt(11)-sqrt(11)sqrt(6))$

$=sqrt(2)/(1-sqrt(6))$

$=(sqrt(2)(1+sqrt(6)))/((1-sqrt(6))(1+sqrt(6)))$

$=(sqrt(2)+sqrt(2)^2sqrt(3))/(1-6)$

$=(sqrt(2)+2sqrt(3))/(-5)$

$=-sqrt(2)/5-(2sqrt(3))/5$

How do you simplify sqrt22/(sqrt11-sqrt66)sqrt22/(sqrt11-sqrt66)?