The side of the square is 5 cm. What is the diagonal of the square?

Let’s mark the vertices with letters ABCD, consider the triangle ABC, the diagonal AC. The sides AB and AC will be 5 cm each. You need to find AC, that is, the hypotenuse of triangle ABC. Let’s find it by the Pythagorean theorem:
5 ^ 2 + 5 ^ 2 = x ^ 2
25 + 25 = x ^ 2
50 = x ^ 2
x = √50
x = √25 * 2
x = 5√2
Answer: the diagonal of the square is 5√2