How do I simplify the following expression?
$\sqrt {k^2+4k}-k-2$
Simplify the following: $\sqrt {k^2+4k}-k-2$
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algebra-precalculus
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0Are you sure any simplification exists? The best thing I can think of is a right triangle with sides k+2, 2, and $\sqrt{k^2+4k}.$ – 2017-01-24
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0You cannot. It's already simplified as much as it can be – 2017-01-24
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0I don't believe your expression can be simplified. At least nothing *obvious* comes to mind. – 2017-01-24
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4I guess the OP is looking for $$-\left[(k+2)-\sqrt{k^2+4k}\right]=-\frac{4}{(k+2)+\sqrt{k^2+4k}}$$ to check that such a number is negative and has the same magnitude of $-\frac{2}{k}$ for large values of $k$. – 2017-01-24
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0@JackD'Aurizio Thank you! – 2017-01-24
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0Jack's comment makes sense. It is also possible to set $j=k+2$ so that the expression $(k+2)\pm \sqrt {k^2+4k}$ becomes $j\pm \sqrt {j^2-4}$ - and this might make it easier to see what is going on. Of course if $k$ is large, so is $j$. – 2017-01-24