$$1.5^2 \times \sqrt{0.0225} = x$$

### Concept & Strategy Solve each part of the expression independently by converting decimals to familiar perfect squares, then multiply the results. ### Step-by-Step Solution * **Given:** The equation $$1.5^2 \times \sqrt{0.0225}$$ * **Calculate Part 1:** Square $1.5$. Ignore the decimal: $15^2 = 225$. Since $1.5$ has $1$ decimal place, $1.5 \times 1.5$ will have $2$ decimal places. $$1.5^2 = 2.25$$ * **Calculate Part 2:** Find $\sqrt{0.0225}$. Ignore the decimal: $\sqrt{225} = 15$. The number $0.0225$ has $4$ decimal places, so its root will have $2$ decimal places. $$\sqrt{0.0225} = 0.15$$ * **Final Multiplication:** Multiply the results. $$2.25 \times 0.15$$ Multiply $225 \times 15 = 3375$. Count the total decimal places: $2$ from $2.25$ and $2$ from $0.15$, giving $4$ total places. $$0.3375$$ ### Exam Strategy & Shortcut Notice that $1.5^2$ and $\sqrt{0.0225}$ are structurally related because $15^2 = 225$. Rewrite as fractions for safer arithmetic: $$(\frac{3}{2})^2 \times \sqrt{\frac{225}{10000}} = \frac{9}{4} \times \frac{15}{100}$$ $$\frac{135}{400} = \frac{33.75}{100} = 0.3375$$ Fractional math often prevents decimal misplacement errors under pressure. ### Common Pitfall * **Mistake:** Misplacing the decimal during the final multiplication ($2.25 \times 0.15$), yielding $0.0375$ or $3.375$. * **Correction:** When multiplying decimals, ALWAYS add up the decimal places of all factors. $2$ places $+ 2$ places MUST equal $4$ places in the final answer. ### Final Answer **Therefore, the correct answer is 0.3375.**