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I'm very rusty... it's been a few years since I've touched radicals and algebra. I had to solve for $k$ in the course of a Physics problem, and I realized I didn't remember how to do this.

$$10=\sqrt{\frac k {0.05}}$$

So I went to Wolfram Alpha and checked the steps. The result was given as 5, but I was confused by this step:

$$10=4.47214 \sqrt k$$

I'm confused by where 4.47214 came from.

Sorry if this is too basic for this forum. I might be missing something that is glaringly obvious...

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    $\begingroup$ $\frac{1}{\sqrt{0.05}}\approx4.47214$ $\endgroup$ – Mufasa Dec 4 '13 at 22:50
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    $\begingroup$ By hand, I would not do it the Alpha way. Square both sides. We get $100=\frac{k}{0.05}$. Now multiply both sides by $0.05$. $\endgroup$ – André Nicolas Dec 4 '13 at 22:52
  • $\begingroup$ Thanks for the quick responses, I understand now. $\endgroup$ – kalexico Dec 4 '13 at 22:54
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Well $1/0.05 = 1/(1/20) = 20$ and so $\sqrt{k/0.05} = \sqrt{20k} = \sqrt{20}\cdot \sqrt{k}$.

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$$10=\sqrt{\frac{k}{0.05}}$$ $$100=\frac{k}{0.05}$$ $$100(0.05)=k$$ $$k=5$$

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