$$\sqrt[2]{x+2x^{2}]{x-2}$$
$\sqrt{x}\left(2\sqrt{x}\sqrt{x-2}+1\right)$
$$\sqrt{x}\left(1+2\sqrt{x}\sqrt{x-2}\right)$$
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$\sqrt{x}\left(2\sqrt{x\left(x-2\right)}+1\right)$