2) \( |\sqrt{5}-3|-|3-\sqrt{5}| \)

Let’s simplify the expression \( |\sqrt{5}-3|-|3-\sqrt{5}| \). First, notice that \( |\sqrt{5}-3| \) and \( |3-\sqrt{5}| \) are essentially the same value but with opposite signs inside the absolute values. Calculating \( |\sqrt{5}-3| \): Since \( \sqrt{5} \) is approximately \( 2.236 \), we have: \[ \sqrt{5}-3 \approx 2.236 - 3 = -0.764 \] Thus, \[ |\sqrt{5}-3| = | -0.764 | = 0.764 \] Now, for \( |3-\sqrt{5}| \): \[ 3-\sqrt{5} \approx 3 - 2.236 = 0.764 \] So, \[ |3-\sqrt{5}| = 0.764 \] Now substituting back into the original expression: \[ |\sqrt{5}-3| - |3-\sqrt{5}| = 0.764 - 0.764 = 0 \] Therefore, the final answer is: \[ \boxed{0} \]