Simplify a radical inside a radical inside a radical

Question

The question is this:

Simplify $\sqrt{1+\sqrt{21+12\sqrt{3}}}$

I defined the value as x, then got $(x+1)^2(x-1)^2$=$21+12\sqrt{13}$.

I don't know what to do from there. Any help?

Answer 1

Hint :

$$21+12 \sqrt{3} = (3+2\sqrt{3})^2$$

and $$4 + 2 \sqrt{3} = (1 + \sqrt{3})^2$$