The length of a diagonal of a square can be calculated using the Pythagorean theorem. For a square, the diagonal divides it into two right-angled triangles. If each side of the square is of length ‘a’, the diagonal ‘d’ can be calculated as:
d = √(a² + a²)
For our square with a side length of 8, the calculation goes as follows:
d = √(8² + 8²)
d = √(64 + 64)
d = √128
d = 8√2
By simplifying, you get approximately:
d ≈ 11.31
So, the length of the diagonal of a square with a side length of 8 is 8√2 or approximately 11.31.