https://docs.google.com/document/d/1eTXrGPcO7BT3k501UyhDe4Ov76SuIerKC35UjmYEuSU/edit?usp=sharing For this question I keep getting 2sqrt 6.?

Not sure where you are picking up the extra times 2 from. I get sqrt 3 for a side of the box and sqrt 6 (approx 2.5) for big circle diameter. And that makes sense because if you put hash marks on a piece of scratch paper the diameter of the big circle and then put hash marks inside of that for dia of the smaller circle about 2.5 small circles would fit into the big one.

Basically I solved the side of a right triangle from the center point of inner circle up to where inner circle touches triangle, added that 0.25 to 0.5 radius. Then I solved the hypotenuse of a right triangle with 0.75 side 30 degrees from that = 0.866 (half of side of triangle or box). Double that = 1.732 (which is your sqrt 3). Solve the diagonal of the box and it is sqrt 6 or 2.449.

I'm finding that the side of the square is 2 sqrt 3, and therefore the diagonal will be the diameter, which the diameter is sqrt 24, or 2sqrt 6. Can you spot a possible mistake, or tell me how to do it please?