Simplifying $\sqrt {11 - 4 \sqrt 7} - \sqrt {8 - 2 \sqrt 7}$ 
$$\sqrt {11 - 4 \sqrt 7} - \sqrt {8 - 2 \sqrt 7} = a$$

I'm having trouble solving this equation. I've tried squaring both sides and got this
$$11 - 4\sqrt{7} - 2 \sqrt{(11 - 4\sqrt{7})(8 - 2\sqrt{7})} + 8 - 2\sqrt{7} = a^2$$
after simplifying
$$19 - 6\sqrt{7} - 2 \sqrt{(11 - 4\sqrt{7})(8 - 2\sqrt{7})} = a^2$$
and that's where I got stuck.

Hint:
$11=(\sqrt7)^2+2^2$  and $\sqrt7-2>0$
$8=(\sqrt7)^2+1^2$ and  $\sqrt7-1>0$
Finally
$$\sqrt{a^2+b^2-2ab}=|a-b|=a-b\text{  if } a-b\ge0$$
