<s>[INST] 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. :(
 [/INST] Square roots obey the rule $\sqrt{a\cdot b}=\sqrt{a}\cdot\sqrt{b}$ .  You wanted to take the $4$ out of $\sqrt{1-4x^2}$.  $1-4x^2=4\cdot\frac{1-4x^2}{4}$.  So $\sqrt{1-4x^2}=\sqrt{4\cdot\frac{1-4x^2}{4}}=\sqrt{4}\cdot\sqrt{\frac{1-4x^2}{4}}=2\cdot\sqrt{\frac{1-4x^2}{4}}$.  I think that's the best explanation I can give.
</s>