Question

Instructions:Select the correct answer from each drop-down menu.

Answer 1

From the figure, the inscribed circle is the circle inside the square. So, the radius of the inscribed circle is half the side of the square. That is 4 cm.

The circumscribed circle is the circle outside the square and its radius is half the diagonal of the square.  Since the square has a side length of 8 cm, the diagonal is computed as follows, using Pythagorean Theorem using half of the square taking the diagonal as the hypotenuse.
     $d=\sqrt{8^2+8^2}=\sqrt{64+64}=\sqrt{128}$

The radius is half the diagonal. So, the radius is
     $\:r=\frac{\sqrt{128}}{2}=\sqrt{\frac{128}{4}}=\sqrt{32}\:$  or (32)^(1/2).

Answer 2

The answer would be 32 ^1/2.

The solution to this is :
D= sqrt 8^2+8^2
=sqrt 64+64
=sqrt 128
R=sqrt 128/2
=sqrt 32
Or 32 ^1/2