1. **Problem Statement:** Determine whether each rational number is a perfect square and evaluate the given square roots. 2. **Recall:** A perfect square is a number that can be expressed as $a^2$ where $a$ is a rational number. 3. **Check each rational number:** a) $0.16 = \frac{16}{100} = \left(\frac{4}{10}\right)^2 = \left(0.4\right)^2$ so it is a perfect square. b) $\frac{90}{49}$: Factor numerator and denominator. $90 = 2 \times 3^2 \times 5$, $49 = 7^2$. Since numerator is not a perfect square (2 and 5 are not squared), $\frac{90}{49}$ is not a perfect square. c) $0.001 = \frac{1}{1000} = \frac{1}{10^3}$. Since the denominator is $10^3$, not an even power, $0.001$ is not a perfect square. d) $\frac{8}{18} = \frac{4 \times 2}{9 \times 2} = \frac{4}{9}$ after canceling 2. $\frac{4}{9} = \left(\frac{2}{3}\right)^2$ so $\frac{8}{18}$ simplifies to a perfect square. 4. **Evaluate:** a) $\sqrt{289} = 17$ since $17^2 = 289$. b) $\sqrt{0.03} = \sqrt{\frac{3}{100}} = \frac{\sqrt{3}}{10} \approx 0.1732$ (irrational, not a perfect square). **Final answers:** - a) $0.16$ is a perfect square. - b) $\frac{90}{49}$ is not a perfect square. - c) $0.001$ is not a perfect square. - d) $\frac{8}{18}$ simplifies to $\frac{4}{9}$ which is a perfect square. - $\sqrt{289} = 17$. - $\sqrt{0.03} \approx 0.1732$ (not a perfect square).