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Math Help - simplifying square roots

  1. #1
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    simplifying square roots

    If r>0 and s>0 and \sqrt{\frac{r}{s}} + \sqrt{\frac{s}{r}} show that \frac{r+s}{\sqrt{rs}} is equivalent.
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  2. #2
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    Hello, donnagirl!

    \text{If }r>0\text{ and }s>0\text{, show that: }\,\sqrt{\dfrac{r}{s}} + \sqrt{\dfrac{s}{r}} \:=\:\dfrac{r+s}{\sqrt{rs}}

    Just add the radicals . . .

    . . \displaystyle \sqrt{\frac{r}{s}} + \sqrt{\frac{s}{r}} \;=\;\frac{\sqrt{r}}{\sqrt{s}} + \frac{\sqrt{s}}{\sqrt{r}} \;=\;\frac{\sqrt{r}\!\cdot\!\sqrt{r} + \sqrt{s}\!\cdot\!\sqrt{s}}{\sqrt{s}\,\sqrt{r}} \;=\;\frac{r + s}{\sqrt{rs}}

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  3. #3
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    OMG soroban, thank you that was just too easy! I was going about it all wrong, I was messing around with the conjugate and such LOL!
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