evaluate \( \sqrt{\frac{0.0048 \times 0.81 \times 10^{-7}}{0.027 \times 0.04 \times 10^{6}}} \)

Let's simplify the expression step by step. First, we can express the problem as follows: \[ \sqrt{\frac{0.0048 \times 0.81 \times 10^{-7}}{0.027 \times 0.04 \times 10^{6}}} \] Calculating the components in the numerator and the denominator separately: 1. **Numerator**: \[ 0.0048 \times 0.81 = 0.003888 \] Thus, the numerator is: \[ 0.003888 \times 10^{-7} = 3.888 \times 10^{-10} \] 2. **Denominator**: \[ 0.027 \times 0.04 = 0.00108 \] Thus, the denominator is: \[ 0.00108 \times 10^{6} = 1.08 \] Now, we can rewrite our expression: \[ \sqrt{\frac{3.888 \times 10^{-10}}{1.08}} \] Next, we calculate the division: \[ \frac{3.888 \times 10^{-10}}{1.08} = 3.600 \times 10^{-10} \quad \text{(approximately)} \] Now, we take the square root: \[ \sqrt{3.600 \times 10^{-10}} = \sqrt{3.600} \times \sqrt{10^{-10}} = \sqrt{3.6} \times 10^{-5} \] Calculating \( \sqrt{3.6} \): \[ \sqrt{3.6} \approx 1.897 \] Putting it all together, we get: \[ 1.897 \times 10^{-5} \] Therefore, the final result is approximately: \[ \sqrt{\frac{0.0048 \times 0.81 \times 10^{-7}}{0.027 \times 0.04 \times 10^{6}}} \approx 1.897 \times 10^{-5} \]