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Math Help - logarithm

  1. #1
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    logarithm

    from what i know, for any positive number a and b, \frac{\sqrt{a}}{\sqrt{b}}=\sqrt{\frac{a}{b}}
    i need to know if it is true all the time, whether i could say that \frac{\sqrt{a}}{\sqrt{b}}=\sqrt{\frac{a}{b}} even when i don't know for sure that a and b is always positive.
    put another way, if i come across a question and my answer is \frac{\sqrt{m}}{\sqrt{n}} where m and n are unknowns and can be any number( even a negative number), do i leave my answer as \frac{\sqrt{m}}{\sqrt{n}}? would it be correct or wrong to to simplify to \sqrt{\frac{m}{n}}?
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  2. #2
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    Re: logarithm

    ps ignore rationalizing for a moment >.< i just want to know if \frac{\sqrt{a}}{\sqrt{b}} always equals \sqrt{\frac{a}{b}}
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