The value of $$\sqrt{0.4}$$ is

### Concept & Formula When finding the square root of a decimal with an odd number of decimal places, convert it to a fraction with a denominator that is a perfect square (like $100$ or $10000$) to accurately estimate the numerator's root. ### Step-by-Step Solution Convert the decimal $0.4$ into a fraction: $$\sqrt{0.4} = \sqrt{\frac{4}{10}}$$ Multiply the numerator and denominator by $10$ to make the denominator a perfect square: $$\sqrt{\frac{40}{100}} = \frac{\sqrt{40}}{\sqrt{100}} = \frac{\sqrt{40}}{10}$$ Estimate the value of $\sqrt{40}$: We know that $6^2 = 36$ and $7^2 = 49$. Since $40$ is closer to $36$, $\sqrt{40} \approx 6.32$. Substitute the estimation back into the fraction: $$\frac{6.32}{10} = 0.632$$ Rounding to two decimal places, we get $0.63$. ### Exam Strategy & Shortcut Never assume $\sqrt{0.4} = 0.2$. Instead, immediately shift the decimal point two places to the right to think in terms of out-of-100: $\sqrt{0.4} = \sqrt{40\%}$. The square root of $40$ is slightly more than $6$, so the decimal answer must be slightly more than $0.6$. Option (d) $0.63$ matches instantly. ### Common Pitfall The most common mistake is incorrectly evaluating $\sqrt{0.4}$ as $0.2$ by ignoring decimal place parity. Remember that $(0.2)^2 = 0.04$, not $0.4$. ### Final Answer **Therefore, the correct answer is 0.63.**