how much does the radius of a circle need to increase to give x more dots in the circle?

Question

the question

so i understand that there would be 13 dots within this circle and it needs 8 more (21 in total) points. The points that needed would be $(+/- 1, +/- 2), (+/- 2, +/- 1)$. but how do you work out the increase in radius needed?

also the answer is radius increase of $\sqrt 5 - 2$

Answer 1

I'm not sure if im suposed to delete the question or add the answer and leave it, but i found the answer.

As the minimum expansion would be at (+/−1,+/−2),(+/−2,+/−1), we can use Pythagoras's theorem to find the new radius.

eg/

2²+1²= r²

so the radius of the new circle would be √5

the increase in radius is therefore √5 - 2, which is the answer