Hello !
You are close to the answer. You have the same one, written in a different form, but you need some more work to get to their actual answer :
$\displaystyle BC^2 = 18 \frac{4}{5} + 4 \sqrt{5} - \frac{12}{\sqrt{5}}$
First, we need to put everything in absolute fraction form (otherwise things get confusing) :
$\displaystyle BC^2 = \frac{94}{5} + 4 \sqrt{5} - \frac{12}{\sqrt{5}}$
Note that you can multiply everything by $\displaystyle 5$ :
$\displaystyle 5 BC^2 = 94 + 20 \sqrt{5} - 12 \sqrt{5}$
Then you can factor a $\displaystyle 2$ out :
$\displaystyle 5 BC^2 = 2 \left (47 + 10 \sqrt{5} - 6 \sqrt{5} \right )$
Simplifying the surds :
$\displaystyle 5 BC^2 = 2 \left (47 + 4 \sqrt{5} \right )$
And finally, dividing by $\displaystyle 5$ :
$\displaystyle BC^2 = \frac{2}{5} \left (47 + 4 \sqrt{5} \right )$
Does it make sense ?
Thank you very much!
If I use my original answer $\displaystyle ( BC^2 = 18\frac{4}{5} + 4\sqrt5 - \frac{12}{\sqrt5} )$ is it still considered to be a correct answer if I use it in, say, a test? Or would it be incorrect because it is not fully simplified?
Thanks.
I believe you might lose some points depending on the context, but it wouldn't be penalized that much unless the question specifically asks for full simplification/factorization. But if you can factorize, do it (here there were two identical surds which sort of looks bad)