The value of $$\sqrt{0.064}$$ is

### Concept & Formula Just like the previous problems, the number $0.064$ has $3$ decimal places (an odd number). Despite containing the perfect square $64$, it will not yield a rational root. Scale to an even number of decimal places. ### Step-by-Step Solution Express as a fraction: $$\sqrt{0.064} = \sqrt{\frac{64}{1000}}$$ Multiply the top and bottom by $10$: $$\sqrt{\frac{640}{10000}} = \frac{\sqrt{640}}{100}$$ Estimate $\sqrt{640}$: We know $25^2 = 625$ and $26^2 = 676$. Since $640$ is exactly between these bounds, $\sqrt{640} \approx 25.29$. Divide by $100$: $$\frac{25.29}{100} = 0.2529$$ Rounding to three decimal places gives $0.252$. ### Exam Strategy & Shortcut Apply the percentage trick: $\sqrt{0.064}$ is the same as $\sqrt{6.4 / 100} = \sqrt{6.4} / 10$. The value of $\sqrt{6.4}$ lies between $\sqrt{4}$ ($2$) and $\sqrt{9}$ ($3$). Specifically, it is around $2.5$. Thus, the final answer must be around $2.5 / 10 = 0.25$. Option (c) is the only mathematical possibility. ### Common Pitfall Seeing "$64$" triggers the urge to select an option containing "$8$", like $0.08$ or $0.8$. However, $(0.8)^2 = 0.64$ and $(0.08)^2 = 0.0064$. Neither equals $0.064$. Count the decimal places! ### Final Answer **Therefore, the correct answer is 0.252.**