$\sqrt{\frac{.0196}{x}} = 0.2$

Concept & Formula Square both sides of the equation immediately to remove the radical, then cross-multiply to isolate the unknown variable in the denominator. Step-by-Step Solution * **Given:** $\sqrt{\frac{0.0196}{x}} = 0.2$ * **Calculation:** Square both sides of the equation to eliminate the square root: $\frac{0.0196}{x} = (0.2)^2$ * Calculate the square of $0.2$: $\frac{0.0196}{x} = 0.04$ * Rearrange the equation to isolate $x$ by swapping $x$ and $0.04$: $x = \frac{0.0196}{0.04}$ * Shift the decimal point two places to the right on both the numerator and denominator to simplify the division: $x = \frac{1.96}{4}$ * Perform the division: $x = 0.49$ Exam Strategy & Shortcut Alternatively, take the square root of the numerator first. $\sqrt{196}$ is $14$. Since it has $4$ decimal places ($0.0196$), the root has $2$ ($0.14$). So, $\frac{0.14}{\sqrt{x}} = 0.2$. Therefore, $\sqrt{x} = \frac{0.14}{0.2} = 0.7$. Squaring both sides yields $x = 0.49$. This avoids dealing with the tiny $0.04$ denominator. Common Pitfall Squaring $0.2$ incorrectly as $0.2$ or $0.004$, which corrupts the final fraction and leads to answers that are off by a factor of 10. Final Answer **Therefore, the correct answer is 0.49.**