$$\sqrt{\frac{0.204 \times 42}{0.07 \times 3.4}}$$ is equal to

### Concept & Formula To simplify expressions involving decimals inside a square root, count the total number of decimal places in the numerator and denominator to eliminate the decimals. ### Step-by-Step Solution Count the decimal places: * Numerator has 3 decimal places (from $0.204$). * Denominator has 3 decimal places ($2$ from $0.07$ and $1$ from $3.4$). Since the number of decimal places is equal, we can remove the decimal points entirely: $$\sqrt{\frac{204 \times 42}{7 \times 34}}$$ Simplify the fraction: * Divide $42$ by $7$: $$\frac{42}{7} = 6$$ * Divide $204$ by $34$: $$\frac{204}{34} = 6$$ Substitute these back into the expression: $$\sqrt{6 \times 6} = \sqrt{36} = 6$$ ### Exam Strategy & Shortcut Count decimal places immediately. Since they balance out ($3$ on top, $3$ on bottom), treat it instantly as an integer problem: $\sqrt{\frac{200 \times 40}{7 \times 30}} \approx \sqrt{\frac{8000}{210}} \approx \sqrt{40} \approx 6$. Looking at the options, $6$ is the only reasonable integer answer. ### Common Pitfall Students often miscount the decimal places or make errors while canceling out numbers, leading to an incorrect power of $10$ such as $0.6$ or $0.06$. Always verify that the decimal shifts in the numerator and denominator balance out perfectly. ### Final Answer **Therefore, the correct answer is 6.**