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Math Help - simplify anymore?

  1. #1
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    simplify anymore?

    <br />
6\sqrt{15} + 9\sqrt{5} -4\sqrt{3} -6 <br />

    Was thinking about
    <br />
6\sqrt{5}\sqrt{3} + 9\sqrt{5} -4\sqrt{3} -6 <br />
    And combine like terms - but something does seem right with the root of 3??
     <br />
15\sqrt{5} -4\sqrt{3} -6  <br />
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  2. #2
    Moo
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    Hello,

    Well the last line is false.

    <br />
6\sqrt{5}\sqrt{3} + 9\sqrt{5} -4\sqrt{3} -6 = \sqrt{5} (6 \sqrt{3}+9) -4\sqrt{3} -6<br />

    I don't think you can simplify more...
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  3. #3
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    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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