Hi kaschwartz!
We can "break down" our last two terms......
\(\displaystyle \L \;\,-\,5\sqrt{3}\,-\,2\sqrt{25}\,-\,2\sqrt{48}\)
\(\displaystyle \L \;\,-\,2\sqrt{5\bullet5}\,-\,2\sqrt{8\bullet6}\)
\(\displaystyle \L \;-\,2\,\bullet5\,-\,2\sqrt{8\bullet6}\)
\(\displaystyle \L \;-\,10\,-\,2\sqrt{2^{3}\bullet2\bullet3\)
\(\displaystyle \L \;\,-\,10\,-\,2\,\bullet\,4\,\bullet\,sqrt{3}\)
\(\displaystyle \L \;-\,5\sqrt{3}\,-\,10\,-\,8sqrt{3}\,\) (Reinserting \(\displaystyle \,-\,5\sqrt{3}\))
\(\displaystyle \L \;\,-\,13\sqrt{3}\,-\,10\)
Now as you can see, what we are trying to do is pull a pair of numbers out of the radical sign, take the number of that pair and multiply by the number outside the radical sign.
For example the numbers in the radical of \(\displaystyle \,-\,2\sqrt{25}\) can be broken down to \(\displaystyle \sqrt{5\bullet5}\,\to\,\sqrt{5^{2}}\) So we pull out the number of the pair, \(\displaystyle 5\), and multiply it by \(\displaystyle \,-\,2\) resulting in \(\displaystyle \,-\,10\)
Whatever is left over stays in the radical and you cannot add terms with radicals unless the have the same radical.
I know this is a lot of info but it'll sink once you set your mind to it. :idea:
