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Math Help - Simplifying square roots?

  1. #1
    Newbie
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    May 2010
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    Simplifying square roots?

    I am having a lot of trouble in my math class.
    I go to school online and am stuck on a particular unit, and my book isn't doing much to helping.

    I normally don't do this, but I am really at a loss and I want to graduate on time. Thanks!

    7.) 3 square root of 2 - 2 square root of 3
    8.) 2 square root of 3 + square root of 27 - square root of 1 / 3
    9.) square root of 3 ( square root of 6 - 2 square root of 3 )
    10.) square root of 1 / 2 x ( square root of 8 + square root of 2 )
    11.) square root of 18 - square root of 3 / square root of 6
    12.) square root of a + square root of b / square root of a - square root of b
    13.) square root of 5 + 1 / square root of 5 - 1
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  2. #2
    Member mohammadfawaz's Avatar
    Joined
    Feb 2010
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    Lebanon - Beirut
    Posts
    100
    7) nothing more to do: 3\sqrt{2}-2\sqrt{3}
    8) 2\sqrt{3}+\sqrt{3^2\times{3}}-\sqrt{\frac{1}{3}}=2\sqrt{3}+3\sqrt{3}-\sqrt{\frac{1}{3}} = 5\sqrt{3}-\sqrt{\frac{1}{3}} = \frac{5\times{3}-1}{\sqrt{3}}=\frac{14\sqrt{3}}{3}
    9) \sqrt{3}(\sqrt{2}\times \sqrt{3}-2\sqrt{3}) = 3\sqrt{2}-6
    10) \sqrt{\frac{1}{2}}(\sqrt{2^2\times 2}+\sqrt{2}) = \frac{1}{\sqrt{2}}(2\sqrt{2}+\sqrt{2}) = 3
    11) \sqrt{3^2\times 2}-\frac{\sqrt{3}}{\sqrt{2}\times \sqrt{3}} = 3\sqrt{2} - \frac{\sqrt{2}}{2} = \frac{5\sqrt{2}}{2}
    12) \frac{\sqrt{a}+\sqrt{b}}{\sqrt{a}-\sqrt{b}} = \frac{(\sqrt{a}+\sqrt{b})(\sqrt{a}+\sqrt{b})}{a-b} = \frac{a+b+2\sqrt{ab}}{a-b}
    13) \sqrt{5}+\frac{1}{\sqrt{5}}-1 = \sqrt{5}+\frac{\sqrt{5}}{5}-1 = \frac{6\sqrt{5}}{5}-1
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  3. #3
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    Thank you so much, man! You are a life saver! =D
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