Help plz, I need explanation

$\sqrt{28 + 16\sqrt{3}}$

If you want to turn that to $a+ b\sqrt{c}$, here's how.

First the c is obviously a 3, because what else would it be duhhh. 

$28 + 16\sqrt{3} = (a + b\sqrt{3})^2 = a^2 + 2ab\sqrt{3} + 3b^2$

$2ab\sqrt{3} = 16\sqrt{3}$ 

$ab = 8$

$a^2 + 3b^2 = 28$

If a and b are integers, you can guess and check a little bit. After some testing, you will find that:

$(a, b) = (4, 2)$

So: $\sqrt{28+16\sqrt{3}} = 4 + 2\sqrt{3}$