If \( \sqrt{3}=1.73 \) evaluate \( \frac{\sqrt{31 \times 7}}{2} \) Correct to 2 d.

To evaluate \( \frac{\sqrt{31 \times 7}}{2} \) and round it to two decimal places, follow these steps: 1. **Calculate the Product Inside the Square Root:** \[ 31 \times 7 = 217 \] 2. **Find the Square Root of 217:** While the exact value of \( \sqrt{217} \) isn't a whole number, we can approximate it. \[ \sqrt{217} \approx 14.73 \] *(This approximation is based on standard square root calculations. Given that \( \sqrt{3} \approx 1.73 \), which is a common approximation, we use standard methods here for simplicity.)* 3. **Divide by 2:** \[ \frac{\sqrt{217}}{2} \approx \frac{14.73}{2} = 7.365 \] 4. **Round to Two Decimal Places:** \[ 7.365 \approx 7.37 \] **Final Answer:** \[ \frac{\sqrt{31 \times 7}}{2} \approx 7.37 \]