Question

How can you write the expression with a rationalized denominator?

(sqrt3-sqrt6) divided by (sqrt3+sqrt6)

Answer 1

multiply top and bottom by \[\Large \sqrt{3}-\sqrt{6}\]

Answer 2

so i got ... 9 – 2 sqrt18

Answer 3

is that right ?

Answer 4

\[\Large (\sqrt{3}-\sqrt{6})(\sqrt{3}-\sqrt{6})\]


\[\Large (\sqrt{3})^2-2*\sqrt{6}*\sqrt{3}+(\sqrt{6})^2\]


\[\Large 3-2*\sqrt{6*3}+6\]


\[\Large 3-2*\sqrt{18}+6\]


\[\Large 9-2*\sqrt{18}\]


Thats in the numerator. In the denominator you have 3 - 6 = -3


So the fraction becomes \[\Large \frac{9-2*\sqrt{18}}{-3}\]


So the final answer would be \[\Large -\frac{9-2*\sqrt{18}}{3}\] which can be written as \[\Large \frac{-9+2*\sqrt{18}}{3}\]

Answer 5

thats not an option.. all there is..

9 – 2 sqrt18
and
-3 -2*sqrt18
divided by
9

Answer 6

and
-1-2*sqrt18
divided by 3

Answer 7

\[\Large \frac{-9+2*\sqrt{18}}{3}\]

\[\Large \frac{-9}{3}+\frac{2*\sqrt{18}}{3}\]

\[\Large -3+\frac{2*\sqrt{18}}{3}\]

Answer 8

thats still not my choices

Answer 9

\[\Large 9-2*\sqrt{18}\] only works if it's divided by -3

Answer 10

so would that be it ???

Answer 11

well there must be a typo somewhere