1. **Simplify the expression $\sqrt{26} - 1$.** Since $\sqrt{26}$ is approximately 5.099, the expression is approximately $$\sqrt{26} - 1 \approx 5.099 - 1 = 4.099.$$ 2. **Prove that $\dfrac{25}{4} = 6.25$ cannot be used to estimate $\sqrt{26}$.** Since $\sqrt{26} \approx 5.099$, $\dfrac{25}{4} = 6.25$ is quite far and overestimates the value. 3. Quantify the difference: $$6.25 - 5.099 = 1.151,$$ which is a large error for estimating $\sqrt{26}$. 4. **Prove that $x_c = 100$ can be used to estimate $\sqrt{26}$.** If $x_c = 100$ is used as a method (perhaps as a squared value), consider: $$\sqrt{26} \approx \sqrt{(100) \times 0.26} = 10 \times \sqrt{0.26}.$$ 5. Estimate $\sqrt{0.26}$: Since $0.25 = \frac{1}{4}$ and $\sqrt{0.25} = 0.5$, $\sqrt{0.26}$ is slightly more than 0.5, approximately 0.51. 6. So: $$10 \times 0.51 = 5.1,$$ which is very close to the true $\sqrt{26} \approx 5.099$. Therefore, using $x_c = 100$ to estimate $\sqrt{26}$ by scaling simplifies and yields a good approximation. **Final answers:** $$\sqrt{26} - 1 \approx 4.099,$$ $\dfrac{25}{4} = 6.25$ is not a good estimate, $x_c = 100$ provides a good approximation to $\sqrt{26}$.