What is the diagonal distance across a square with side 1 unit?

Let the length of the diagonal be d and the side of the square be a.

So, from the Pythagoras Theorem,

d² = a² + a²

⇒ d² = 1² + 1²

⇒ d² = 2

⇒ d = √2

⇒ d = 1.414 units

Therefore, the diagonal distance across a square with side 1 unit is 1.414 units.