1. **State the problem:** Calculate the value of the expression $7 \times 0.007 \times \sqrt{0.0435}$.\n\n2. **Recall the formula and rules:**\n- Multiplication of decimals is straightforward: multiply the numbers as if they were whole numbers, then place the decimal point in the product.\n- The square root function $\sqrt{x}$ gives the number which, when squared, equals $x$.\n\n3. **Calculate the square root:**\nCalculate $\sqrt{0.0435}$. Using a calculator or approximation, $\sqrt{0.0435} \approx 0.2085$.\n\n4. **Multiply the decimals:**\nFirst multiply $7 \times 0.007 = 0.049$.\nThen multiply $0.049 \times 0.2085$.\nCalculate: $0.049 \times 0.2085 = 0.0102165$.\n\n5. **Final answer:**\nThe value of the expression $7 \times 0.007 \times \sqrt{0.0435}$ is approximately $0.0102$ (rounded to four decimal places).