Question 53688
By the pythagorean theorem, about the sides of a right triangle:

{{{a^2 + b^2 = c^2}}}, where c is the hypotenuse.

If you ignore two sides of a square, the remaining two sides and the diagonal form a right triangle. Since both sides we consider are equal, and we know the length of the diagonal, let's modify our equation a bit:

{{{2a^2 = (8sqrt(2))^2}}}

Distribute the exponentiation and solve:

{{{2a^2 = 8^2*sqrt(2)^2}}}
{{{2a^2 = 128}}} 
{{{a^2 = 64}}}
{{{a = -8}}} or {{{a = 8}}}

Since the length of the side of an square has to be positive, the sides of the square measure 8.