The surface are of a cube with side s is given by the expression 6*s^2.
Here we have the surface area as 186 square inches
6*s^2 = 186
s^2 = 31
=> s = sqrt 31
=> 5.5677 (approximately)
The side of the cube has a length 5.5677 inches.
The number of like faces of the cube is 6.
We'll note the length of the side of the cube as a.
The area of a face is:
A = a^2
Since there are 6 faces, we'll get the total area:
S = 6a^2
186 = 6a^2
We'll divide by 6:
a^2 = 31
a = sqrt 31
a = 5.567 inches
We'll validate just the positive value for the length.