1. **State the problem:** We need to estimate $\sqrt{0.05}$ to the nearest hundredth using a number line, then calculate it to the nearest thousandth. 2. **Recall the formula:** The square root function $\sqrt{x}$ gives a number which, when multiplied by itself, equals $x$. 3. **Estimate using a number line:** - Note that $0.05$ is between $0$ and $0.1$. - We know $\sqrt{0.04} = 0.2$ and $\sqrt{0.09} = 0.3$. - Since $0.05$ is closer to $0.04$ than $0.09$, $\sqrt{0.05}$ is slightly above $0.2$. - So, an estimate to the nearest hundredth is $0.22$. 4. **Calculate to the nearest thousandth:** - Use a calculator or approximate: $$\sqrt{0.05} = \sqrt{\frac{5}{100}} = \frac{\sqrt{5}}{10}.$$ - Since $\sqrt{5} \approx 2.236$, then $$\sqrt{0.05} \approx \frac{2.236}{10} = 0.2236.$$ - Rounded to the nearest thousandth, this is $0.224$. **Final answers:** - Estimated to the nearest hundredth: $0.22$ - Calculated to the nearest thousandth: $0.224$