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Math Help - surd algebra help

  1. #1
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    surd algebra help

    express  \sqrt{22.5} in the form  K\sqrt{10}

    I dont get how to do this, can some one show me? Thanks.
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  2. #2
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    Quote Originally Posted by Tweety View Post
    express  \sqrt{22.5} in the form  K\sqrt{10}

    I dont get how to do this, can some one show me? Thanks.
    Recall that
    \sqrt{ab} = \sqrt{a} \sqrt{b}

    \sqrt{a^2} = a

    \sqrt{22.5} = K\sqrt{10} = \sqrt{10K^2}

    Square both sides:

    10K^2 = 22.5

    solve for K
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  3. #3
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    \sqrt{22.5} = \sqrt{2.25 \cdot 10} = \sqrt{2.25} \cdot \sqrt{10}
    So K=\sqrt{2.25} = \frac{3}{2}
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  4. #4
    A riddle wrapped in an enigma
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    Quote Originally Posted by Tweety View Post
    express  \sqrt{22.5} in the form  K\sqrt{10}

    I dont get how to do this, can some one show me? Thanks.
    Hi Tweety,

    Another approach:

    \sqrt{22.5}=\sqrt{\frac{225}{10}}=15\sqrt{\frac{1}  {10}}=\frac{15\sqrt{10}}{10}=\frac{3}{2}\sqrt{10}
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  5. #5
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    the correct answer is  \frac{3}{2}\sqrt{10}
    edit; oh right I get it now, thanks!
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  6. #6
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by Tweety View Post
    the correct answer is  \frac{3}{2}\sqrt{10}
    edit; oh right I get it now, thanks!
    The square root of 2.25 is 1.5
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