Divide inside a Radical It has been so long since I have done division inside of radicals that I totally forget the "special rule" for for doing it. -_-
For example, say I wanted to divide the 4 out of this expression:

$\sqrt{1 - 4x^2}$

Is this the right way to go about it?

$\frac{16}{16} \cdot \sqrt{1 - 4x^2}$
$16 \cdot \frac{\sqrt{1 - 4x^2}}{16}$
$16 \cdot \sqrt{\frac{1 - 4x^2}{4}} \Longleftarrow \text{Took the square root of 16 to get it in the radicand as the divisor}$

I know that this really a simple, question. Can't believe that I forgot how to do it. :(

The correct way to do this, after fixing the mistake pointed out by Donkey_2009, is:

$\dfrac{2}{2} \cdot \sqrt{1-4x^2}$
$= 2 \cdot \dfrac{\sqrt{1-4x^2}}{2}$
$= 2 \cdot \dfrac{\sqrt{1-4x^2}}{\sqrt{4}} \qquad \Leftarrow$ applied $x = \sqrt{x^2}$
$= 2 \cdot \sqrt{\dfrac{1-4x^2}{4}} \qquad \Leftarrow$ applied $\frac{\sqrt a}{\sqrt b} = \sqrt{\frac a b}$

