Let the side of the square be a. Inradius of square = side of square/2 = a/2 ⇒ Circumradius of square = diagonal of square/2 ⇒ Circumradius of square = (√2 × side of square)/2 = (√2a)/2 ⇒ Inradius of square : Circumradius of square = (a/2) : (√2a/2) = 1 : √2 ∴ The ratio of the inradius and circumradius of a square is 1 : √2.