1. **State the problem:** Find the value of $\sqrt{287}$. 2. **Recall the definition:** The square root of a number $x$ is a value $y$ such that $y^2 = x$. 3. **Estimate the square root:** Since $17^2 = 289$ and $16^2 = 256$, $\sqrt{287}$ is between 16 and 17. 4. **Approximate:** Because 287 is closer to 289 than 256, $\sqrt{287}$ is slightly less than 17. 5. **Use a calculator or approximation method:** $\sqrt{287} \approx 16.94$. **Final answer:** $$\sqrt{287} \approx 16.94$$