Nested decimal radicals simplification: Evaluate √[(0.324 × 0.081 × 4.624) / (1.5625 × 0.0289 × 72.9 × 64)].

Introduction / Context:This expression looks complicated but becomes simple when decimals are written as exact fractions and factors are canceled before taking the square root.

Given Data / Assumptions:

• Numerator: 0.324, 0.081, 4.624.
• Denominator: 1.5625, 0.0289, 72.9, 64.
• All are exact decimals (e.g., 1.5625 = 25/16; 0.0289 = 17^2/10^4).

Concept / Approach:Convert to prime-powered fractions, cancel common factors systematically, then take the square root at the end to avoid rounding.

Step-by-Step Solution:

Verification / Alternative check:Compute numerically with high precision: result ≈ 0.02400, confirming the exact fractional outcome.

Why Other Options Are Wrong:

• 24 and 2.40 are off by factors of 1000 and 100.
• “None of these” is unnecessary since 0.024 matches exactly.
• 0.12 is five times too large.

Common Pitfalls:Rounding mid-steps instead of canceling exactly; mixing percent and decimal interpretations.

Final Answer:0.024