1. **State the problem:** Find the value of $$\left(\sqrt{\frac{6.231}{242.7}}\right)^3$$ using logarithm tables. 2. **Rewrite the expression:** Let $$x = \frac{6.231}{242.7}$$. Then the expression becomes $$\left(\sqrt{x}\right)^3 = x^{\frac{3}{2}}$$. 3. **Calculate the logarithm of $$x$$:** $$x = \frac{6.231}{242.7} \approx 0.02568$$ 4. **Find $$\log x$$:** Using log tables or approximation, $$\log 0.02568 = \log (2.568 \times 10^{-2}) = \log 2.568 + \log 10^{-2} = 0.4097 - 2 = -1.5903$$ 5. **Multiply by the power $$\frac{3}{2}$$:** $$\log y = \frac{3}{2} \times (-1.5903) = -2.38545$$ 6. **Find the antilog:** $$y = 10^{-2.38545} = 10^{-3 + 0.61455} = 10^{-3} \times 10^{0.61455}$$ From log tables, $$10^{0.61455} \approx 4.12$$ 7. **Final value:** $$y \approx 4.12 \times 10^{-3} = 0.00412$$ **Answer:** $$\left(\sqrt{\frac{6.231}{242.7}}\right)^3 \approx 0.00412$$