The diagonal of a square is 5√2

units. What is the side length of the square?

It's an application of the Pythagorean theorem. Remember that a square has all sides the same length. Then, the diagonal can be the hypotenuse of a right triangle and the square's two sides will be the triangle's legs.

(side length) ^2 * 2 = (diagonal) ^2

diagonal^2 = (5*sqrt (2)) ^2 = sqrt (50) ^2 = 50

(side length) ^2 * 2 = 50

(side length) ^2 = 25

side length = sqrt (25) = 5