To simplify the expression \(\sqrt{\frac{(0.0023 \times 750)}{(0.00345 \times 1.25)}}\), we will follow a step-by-step approach. ### Step 1: Calculate the Numerator First, we need to calculate the numerator of the fraction: \[ 0.0023 \times 750 \] Calculating this: \[ 0.0023 \times 750 = 1.725 \] ### Step 2: Calculate the Denominator Next, we calculate the denominator of the fraction: \[ 0.00345 \times 1.25 \] Calculating this: \[ 0.00345 \times 1.25 = 0.0043125 \] ### Step 3: Form the Fraction Now we can form the fraction: \[ \frac{1.725}{0.0043125} \] ### Step 4: Perform the Division Next, we perform the division: \[ \frac{1.725}{0.0043125} = 400 \] ### Step 5: Take the Square Root Now we take the square root of the result: \[ \sqrt{400} = 20 \] ### Conclusion Thus, the simplified value of the original expression \(\sqrt{\frac{(0.0023 \times 750)}{(0.00345 \times 1.25)}}\) is **20**. ### Explanation of Options - **Option A: 15** - This is incorrect because the calculations show that the result is much higher than 15. - **Option B: 20** - This is the correct answer as we have calculated. - **Option C: 40** - This is incorrect; the square root of 400 is not 40, but 20. - **Option D: 75** - This is also incorrect; the calculations do not support this value. ### Summary - We calculated the numerator and denominator separately. - We formed the fraction and performed the division. - We took the square root of the result to find the final answer. - The correct answer is **20**. ### Revision Summary - Always calculate the numerator and denominator separately before forming a fraction. - Ensure to perform division accurately. - Remember to take the square root of the final result. - Double-check calculations to avoid common pitfalls in arithmetic.