Sunday, April 30, 2017

algebra precalculus - How does $frac12sqrt{n^2 + frac{4m^3}{27}}$ become $sqrt{frac{n^2}4 + frac{m^3}{27}}$?



$$\begin{align}
&\frac n2 \pm \frac12 \,\sqrt{n^2 + \frac{4m^3}{27}}\\[6pt]
=\; &\frac n2 \pm \phantom{\frac12}\sqrt{\frac{n^2}4 + \frac{m^3}{27}}
\end{align}$$




Can someone please explain me how this radical multiplied by $1/2$ becomes this? You can see $1/2$ disappeared, and division by $4$ appeared under square root.



Thanks.

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