# Math Help - simplify anymore?

1. ## simplify anymore?

$
6\sqrt{15} + 9\sqrt{5} -4\sqrt{3} -6
$

$
6\sqrt{5}\sqrt{3} + 9\sqrt{5} -4\sqrt{3} -6
$

And combine like terms - but something does seem right with the root of 3??
$
15\sqrt{5} -4\sqrt{3} -6
$

2. Hello,

Well the last line is false.

$
6\sqrt{5}\sqrt{3} + 9\sqrt{5} -4\sqrt{3} -6 = \sqrt{5} (6 \sqrt{3}+9) -4\sqrt{3} -6
$

I don't think you can simplify more...

$6\sqrt{5}\sqrt{3} + 9\sqrt{5} -4\sqrt{3} -6 = \sqrt{5} (6 \sqrt{3}+9) -4\sqrt{3} -6$.

Note now that $6\sqrt{3}+9=3(2\sqrt{3}+3)$ and $-4\sqrt{3}-6=-2(2\sqrt{3}+3)$.
Thus:
$6\sqrt{15}+9\sqrt{5}-4\sqrt{3}-6=3\sqrt{5}(2\sqrt{3}+3)-2(2\sqrt{3} +3)$
$\,\,\,\,=(3\sqrt{5}-2)(2\sqrt{3}+3)$.

--Kevin C.