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Thread: Simplifying surds

  1. #1
    Junior Member
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    Simplifying surds

    Hi,

    Can these examples be simplified any futher or is there an easier way to write them?

    a=5

    e = \sqrt{1-15/25} =\sqrt{2/5}

    a/e = 5/\sqrt{2/5}

    ae = 5\times\sqrt{2/5}

    Thanks, I find these really difficult
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  2. #2
    MHF Contributor

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    Quote Originally Posted by cozza View Post
    Hi,

    Can these examples be simplified any futher or is there an easier way to write them?

    a=5

    e = \sqrt{1-15/25} =\sqrt{2/5}

    a/e = 5/\sqrt{2/5}
    You can "rationalize the denominator": multiply both numerator and denominator to get \frac{5\sqrt{2/5}}{2/5}= \frac{25\sqrt{2/5}}{2}

    ae = 5\times\sqrt{2/5}

    Thanks, I find these really difficult
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  3. #3
    Senior Member Stroodle's Avatar
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    Hi there.

    \sqrt{1-\frac{15}{25}}=\sqrt{\frac{10}{25}}=\frac{\sqrt{10  }}{\sqrt{25}}=\frac{\sqrt{10}}{5}

    so,

    5\div \frac{\sqrt{10}}{5}=5\times\frac{5}{\sqrt{10}}=\fr  ac{25}{\sqrt{10}}=\frac{25\sqrt{10}}{10}=\frac{5\s  qrt{10}}{2}

    and

    5\times\frac{\sqrt{10}}{5}=\sqrt{10}
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