Compute the value of √[ (0.324 × 0.081 × 4.624) / (1.5625 × 0.0289 × 72.9 × 64 ) ].

Introduction / Context:
This evaluation problem blends decimal arithmetic with a square root. Recognizing familiar squares among decimals (like 1.5625 = 1.25^2, 0.0289 = 0.17^2, 64 = 8^2) can simplify the process, but careful computation also works.

Given Data / Assumptions:

• Expression inside the square root: (0.324 × 0.081 × 4.624) / (1.5625 × 0.0289 × 72.9 × 64).
• All positive values, so the principal square root applies.

Concept / Approach:
Multiply the numerators and denominators separately; then take the square root. When possible, group terms as squares to reduce effort. Keep track of place values to avoid scaling errors.

Step-by-Step Solution:
Compute numerator: 0.324 × 0.081 × 4.624 = 0.121352256 (rounded at the end if needed).Compute denominator: 1.5625 × 0.0289 × 72.9 × 64 = 210.681 (approx.).Form the ratio: ≈ 0.121352256 / 210.681 ≈ 0.000576.Square root: √0.000576 = 0.024.

Verification / Alternative check:
Note 0.0289 = 0.17^2, 1.5625 = 1.25^2, and 64 = 8^2. If the remaining product reduces to 0.000576, the square root must be 0.024, confirming the result without a calculator by recognizing 24^2 = 576 and adjusting for decimal places.

Why Other Options Are Wrong:
24 and 2.4: Off by multiple powers of 10; they ignore small decimal outcomes.None of these and 0.24: Do not match the correctly computed 0.024.

Common Pitfalls:
Premature rounding before taking the square root; mishandling decimal places; not simplifying with perfect square recognitions that speed up checking.

Final Answer:
0.024