Question

You measure two quantities as \( A = 1.0 \,m \pm 0.2 \,m \), \( B = 2.0 \,m \pm 0.2 \,m \). We should report the correct value for \( \sqrt{AB} \) as:

• A. \( 1.4 \,m \pm 0.4 \,m \)
• B. \( 1.41 \,m \pm 0.15 \,m \)
• C. \( 1.4 \,m \pm 0.3 \,m \)
• D. \( 1.4 \,m \pm 0.2 \,m \)

Hint:

For multiplication or division, relative errors are added. The formula for error propagation in square roots is: \[ \frac{\Delta Y}{Y} = \frac{1}{2} \left( \frac{\Delta A}{A} + \frac{\Delta B}{B} \right). \]