What is the radius of the circumscribed circle about a square if the side of the square is a (for example, a≈6).

Answer: the radius of the circumscribed circle at a = 6 will be ≈ 4.24.
If we draw a square and draw two diagonals inside it, then when they intersect, they divide each other into two equal parts. The intersection point will be the center of the circumscribed circle and lie in the middle of the hypotenuse of any of the triangles obtained by drawing any of the diagonals. The distance from this point to any of the vertices will be the desired radius.
By the Pythagorean theorem, we determine the length of the hypotenuse c, taking into account that in our case the legs are 6.
6 ^ 2 + 6 ^ 2 = 72.
c = √72 ≈ 8.48.
Determine the radius
8.48 / 2 ≈ 4.24.