If sqrt{96}/2 = k(sqrt{6}), find k.
I multiplied both sides by 2 and got
sqrt{96} = 2k(sqrt{6})
Do I now divide both sides by 2(sqrt{6}) to find k?
Yes, you can do that, though when you try to solve these problems, do not add terms to the side with the variable you are trying to isolate.
I mean that you want to get things away from the "k", at least in this stage of the game.
To save you time, don't do the first step, but instead just do this:
$\displaystyle (1/\sqrt{6}) \times (\sqrt{96}/2) = (k\sqrt{6}) \times (1/\sqrt{6})$
$\displaystyle \sqrt{16}/2 = k$
$\displaystyle 4/2 = k$
k=2
have fun