Is the diagonal of a square the same length as the side? 

The length of the diagonal of the square is equal to √2 times of its side.

Answer: No, the diagonal of a square is not the same length as the side.

We will use the Pythagoras theorem for finding the length of the diagonal of a square.

Explanation:

The diagonal of a square form a right-angled triangle with any two adjacent sides of the square. Diagonal is the hypotenuse and the two sides of the square are perpendicular and base of the right-angled triangle.

By Pythagorus theorem, Hypotenuse² = Perpendicular² + Base² 

Hence, Diagonal² = Side² + Side²

Diagonal = √2 × Side

Hence, the diagonal of a square is not the same length as the side because the length of the diagonal of the square is equal to √2 times of its side.