A difference of two growing roots

Evaluate $\displaystyle\lim_{x\to \infty}\left(\sqrt{x^2+3x}\;-\;x\right)$ . Give a decimal to two places.

Show hints (2)+

It's $\infty-\infty$ : multiply by the conjugate $\sqrt{x^2+3x}+x$ .
You get $\tfrac{3x}{\sqrt{x^2+3x}+x}$ ; divide top and bottom by $x$ and let $x\to\infty$ .

Answer

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1.5

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