I think this goes here.

$\displaystyle a \epsilon \mathbb{R} \text{ and }0<a<1 \Rightarrow

0<1-\sqrt{1-a}<a$

I'm not sure where to start with this proof, rather i'm not sure where to start with this proof if I do not use the fact that I can square both sides.

because I think: $\displaystyle {a^2}<{1^2}$