The problem asks us to find the length of the diagonal of a square whose side length is 6. The diagonal is denoted as $c$.

1. Problem Description

The problem asks us to find the length of the diagonal of a square whose side length is

6. The diagonal is denoted as $c$.

2. Solution Steps

Let the side length of the square be $s$, which is given as

6. Let the length of the diagonal be $d$. The diagonal divides the square into two right-angled triangles. We can use the Pythagorean theorem to find the length of the diagonal.

The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the diagonal is the hypotenuse, and the two sides of the square are the other two sides of the right-angled triangle. Thus, we have:

$d^2 = s^2 + s^2$

Since $s=6$, we have:

$d^2 = 6^2 + 6^2$

$d^2 = 36 + 36$

$d^2 = 72$

$d = \sqrt{72}$

3. Final Answer

$\sqrt{72}$