squares have 4 equal sides. area of square is the square of a side.
Area = side x side
if side = x
the area of the square is 1/64 square miles
1/64 = x * x

when multiplying fractions, numerators are mulitiplied by numerators and denominators by denominators

the square root of the denominator 64 is 8.
therefore
side length = 1/8 miles