1. **State the problem:** We need to select all the squares in order from least to greatest based on the numerical values of the expressions inside them. 2. **Evaluate each expression:** - $\infty$ is infinite, so it is the greatest. - $\sqrt{2} \approx 1.414$ - $e^5 \approx 148.413$ - $\log_4(20)$: Use change of base formula $\log_4(20) = \frac{\log(20)}{\log(4)}$. Using natural logs, $\log(20) \approx 2.9957$, $\log(4) \approx 1.3863$, so $\log_4(20) \approx \frac{2.9957}{1.3863} \approx 2.16$ - $\int_2^5 x \, dx$: Calculate the definite integral. $$\int_2^5 x \, dx = \left[ \frac{x^2}{2} \right]_2^5 = \frac{5^2}{2} - \frac{2^2}{2} = \frac{25}{2} - \frac{4}{2} = \frac{21}{2} = 10.5$$ - $2! = 2 \times 1 = 2$ - $\frac{6\pi}{4} = \frac{3\pi}{2} \approx 3 \times 1.5708 = 4.712$ - $\frac{5}{10} = 0.5$ - $\sum_{i=1}^2 i = 1 + 2 = 3$ 3. **Order the values from least to greatest:** $$0.5 < 1.414 < 2 < 3 < 4.712 < 10.5 < 2.16 < 148.413 < \infty$$ Note: $\log_4(20) \approx 2.16$ is actually between 2 and 3, so the correct order is: $$0.5 < 1.414 < 2 < 2.16 < 3 < 4.712 < 10.5 < 148.413 < \infty$$ 4. **Match these values to the expressions:** - $0.5$ is $\frac{5}{10}$ - $1.414$ is $\sqrt{2}$ - $2$ is $2!$ - $2.16$ is $\log_4(20)$ - $3$ is $\sum_{i=1}^2 i$ - $4.712$ is $\frac{6\pi}{4}$ - $10.5$ is $\int_2^5 x \, dx$ - $148.413$ is $e^5$ - $\infty$ is $\infty$ **Final answer:** The squares in order from least to greatest are: $$\frac{5}{10}, \sqrt{2}, 2!, \log_4(20), \sum_{i=1}^2 i, \frac{6\pi}{4}, \int_2^5 x \, dx, e^5, \infty$$