Evaluate an exact fractional square root: Compute √(36.1 / 102.4) and express it as a simplified fraction.

Introduction / Context:Converting decimals to exact fractional forms often reveals perfect-square structure. Here, we simplify inside the radical first, then take the square root.

Given Data / Assumptions:

• Expression: √(36.1 / 102.4).
• Decimals are exact terminating decimals convertible to fractions.

Concept / Approach:Multiply numerator and denominator to remove decimals and look for squares. Note that 36.1/102.4 = 361/1024 after scaling by a factor of 10 in numerator and denominator.

Step-by-Step Solution:

Verification / Alternative check:Compute (19/32)^2 = 361/1024 = 36.1/102.4, confirming exactness.

Why Other Options Are Wrong:

• 29/32 and 29/62 have incorrect numerators/denominators.
• 19/72 does not square to 361/1024.
• “None of these” is not needed since 19/32 appears.

Common Pitfalls:Mis-scaling decimals or taking the square root of 1024 wrongly. Remember 1024 = 2^10, so √1024 = 32.

Final Answer:19/32