Given that $\sqrt{13} = 3.605$ and $\sqrt{130} = 11.40$, find the value of $\sqrt{1.3} + \sqrt{1300} + \sqrt{0.013}$.

Concept & Strategy When adjusting square roots by powers of $10$, you must shift by even powers of $10$ (like $100$ or $10000$) to properly move values in and out of the square root. Use either $\sqrt{13}$ or $\sqrt{130}$ depending on which provides an even decimal shift. Step-by-Step Solution * **Given:** $\sqrt{13} = 3.605$ and $\sqrt{130} = 11.40$. * **Calculation:** Manipulate each term into a known value divided or multiplied by $100$ or $10000$: * $\sqrt{1.3} = \sqrt{\frac{130}{100}} = \frac{\sqrt{130}}{\sqrt{100}} = \frac{11.40}{10} = 1.14$ * $\sqrt{1300} = \sqrt{13 \times 100} = \sqrt{13} \times 10 = 3.605 \times 10 = 36.05$ * $\sqrt{0.013} = \sqrt{\frac{130}{10000}} = \frac{\sqrt{130}}{\sqrt{10000}} = \frac{11.40}{100} = 0.114$ * Sum the evaluated terms: $1.14 + 36.05 + 0.114 = 37.304$ Exam Strategy & Shortcut Focus heavily on the largest number to estimate. $\sqrt{1300}$ is approximately $36$. The other terms ($\approx 1.1$ and $\approx 0.1$) add a small fraction. The sum must be around $37.2$ or $37.3$. Option (d) $37.304$ is the only perfectly matching candidate. Common Pitfall Incorrectly converting $\sqrt{1.3}$ using $\sqrt{13}$ instead of $\sqrt{130}$ (e.g., writing it as $\sqrt{13/10}$ which leaves a $\sqrt{10}$ in the denominator, making it unnecessarily complex). Final Answer **Therefore, the correct answer is 37.304.**