C = \sqrt{A^{2} + B^{2}}

\begin{aligned}A & = 5.3 ± 0.2 cm \\ B & = 15.4 ± 0.3 cm \end{aligned}

if C = \sqrt{A^{2} + B^{2}} , what is ΔC?

\frac{ΔA^{2}}{A^{2}} = \frac{ΔA}{A} + \frac{ΔA}{A}

= \frac{0.2}{5.3} + \frac{0.2}{5.3}

= 0.075

ΔA^{2} = 0.075A^{2} = 2.1 cm^{2}

A^{2} = 28.1 ± 2.1 cm^{2}

B^{2} = 237.2 ± 9.2 cm^{2}

C^{2} = A^{2} + B^{2} = 265.3 ± 11.3 cm^{2}

\frac{ΔC^{2}}{C^{2}} = \frac{11.3}{265.3} = 0.043

\begin{aligned}\frac{ΔC}{C} & = \frac{1}{2} \frac{ΔC^{2}}{C^{2}} \\ & = 0.021 \end{aligned}

ΔC = 0.02 C = 0.021 (16.3 cm) = 0.3 cm

C = 16.3 ± 0.3 cm