How to get from $a\sqrt{1 + \frac{b^2}{a^2}}$ to $\sqrt{a^2 + b^2}$ I have the following expression: $a\sqrt{1 + \frac{b^2}{a^2}}$.  If I plug this into Wolfram Alpha, it tells me that, if $a, b$ are positive, this equals $\sqrt{a^2 + b^2}$.
How do I get that result?  I can't see how that could be done.  Thanks

$$a\sqrt{1 + \frac{b^2}{a^2}}$$
$$=a\sqrt{\frac{a^2 + b^2}{a^2}}$$
$$=a\frac{\sqrt{a^2 + b^2}}{|a|}$$
So when $a$ and $b$ are positive, $|a|=a$. Hence:
$$=\sqrt{a^2 + b^2}$$
Without the assumption: 
$$\sqrt{a^2} =|a|=\begin{cases}   a   && a \geq 0\\   -a &&a < 0\\   \end{cases}$$
