For a square with side length s, the length of the diagonal d can be found using the Pythagorean theorem: d² = s² + s².

For a square with side length $s = 4 \text{ cm}$, the diagonal $d$ is given by:

$$d^2 = s^2 + s^2$$ $$d^2 = (4 \text{ cm})^2 + (4 \text{ cm})^2$$ $$d^2 = 16 \text{ cm}^2 + 16 \text{ cm}^2$$ $$d^2 = 32 \text{ cm}^2$$

$$d = \sqrt{32} \text{ cm}$$ $$d = \sqrt{16 \times 2} \text{ cm}$$ $$d = 4\sqrt{2} \text{ cm}$$

Using $\sqrt{2} \approx 1.4142$:

$$d \approx 4 \times 1.4142 \text{ cm}$$ $$d \approx \boxed{5.657 \text{ cm}}$$

The error in your work was in the simplification of $\sqrt{32}$. It should be $4\sqrt{2}$, not $\sqrt{112}$. Also, the line $d = 4 \times 4 \text{ cm}$ was incorrect.