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Math Help - surd/radical simplification

  1. #1
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    surd/radical simplification

    I am looking to simplify this radical/surd a model/method for future use would be appreciated 5√78√52 I am hoping to put together a lot of basic questions as models to help people many thanks in advance
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  2. #2
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    Re: surd/radical simplification

    Quote Originally Posted by unkle View Post
    I am looking to simplify this radical/surd a model/method for future use would be appreciated 5√78√52 I am hoping to put together a lot of basic questions as models to help people many thanks in advance
    FACTOR:
    78=2\cdot 3\cdot 13~\&~52=2^2\cdot 13.
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  3. #3
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    Re: surd/radical simplification

    please could you write that as a product of an integer so I can show the working out many thanks in advance
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  4. #4
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    Re: surd/radical simplification

    \sqrt{78}\times\sqrt{52}

    Factorise the values into their smallest terms
    78=2\times 3\times 13, 52= 2\times 2\times 13

    put them back under the square root in the factorised form
    \sqrt{2\times 3\times 13}\times\sqrt{2\times 2\times 13}

    You can bring the two square roots together
    \sqrt{2\times 3\times 13\times 2\times 2\times 13}

    Bring like factors together
    \sqrt{2^3\times 3\times 13^2}

    Remember the rules for manipulating square roots
    \sqrt{2^3}\times \sqrt{3}\times \sqrt{13^2}

    The square root sign goes away if something is squared
    2\sqrt{2}\times \sqrt{3}\times 13

    And bring it back to one square root
    26\sqrt{6}
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