A strong 1:1 electrolyte has Λm = 140.6 S cm²/mol at 0.0064 mol/L and Λm = 134.2 S cm²/mol at…

Step 1. The square roots. $\sqrt{0.0064} = 0.080$ and $\sqrt{0.0256} = 0.160$ in $(\text{mol/L})^{1/2}$.

Step 2. The slope. $A = \dfrac{140.6 - 134.2}{0.160 - 0.080} = 80.0\ \text{S cm}^2\,\text{mol}^{-1}$ for each $(\text{mol/L})^{1/2}$.

Step 3. The intercept. $\Lambda_m^\circ = 140.6 + 80.0 \times 0.080 = 147.0\ \text{S cm}^2/\text{mol}$.

Step 4. The new concentration. $\sqrt{0.0576} = 0.240$, so $\Lambda_m = 147.0 - 80.0 \times 0.240 = 127.8\ \text{S cm}^2/\text{mol}$.