simplify anymore?

**mathobust** · March 22nd 2008, 01:12 PM

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

Was thinking about
$ 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 $

**Moo** · March 22nd 2008, 01:16 PM

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...

**TwistedOne151** · March 22nd 2008, 04:35 PM

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

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.

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