1. First, understand the problem: Calculate $\sqrt{7164} \times 0.082$ without using logarithms, using a tabular method. 2. Estimate $\sqrt{7164}$. Since $85^2 = 7225$ and $84^2 = 7056$, $\sqrt{7164}$ is approximately between 84 and 85. 3. Using linear interpolation: $$ \sqrt{7164} \approx 84 + \frac{7164 - 7056}{7225 - 7056} = 84 + \frac{108}{169} \approx 84 + 0.639 = 84.639 $$ 4. Multiply by 0.082: $$ 84.639 \times 0.082 = 6.939998 \approx 6.94 $$ 5. Therefore, the answer is approximately $6.94$. | Step | Operation | Result | |-------|----------------------------|---------| | 1 | Estimate $\sqrt{7164}$ | Between 84 and 85 | | 2 | Calculate approximate value | $84.639$ | | 3 | Multiply by 0.082 | $6.94$ |