Evaluate the expression √(1.21 × 0.9) ÷ √(1.1 × 0.11) and provide the exact simplified value.

Introduction / Context:
This tests manipulating radicals and recognizing that √a / √b = √(a/b). Arithmetic with decimals is straightforward when converted to fractions or simplified decimals.

Given Data / Assumptions:

• Compute √(1.21 × 0.9) / √(1.1 × 0.11).

Concept / Approach:
Combine the radicals: √(1.21 × 0.9) / √(1.1 × 0.11) = √[(1.21 × 0.9) / (1.1 × 0.11)]. Then simplify the quotient inside the square root.

Step-by-Step Solution:
Compute numerators/denominators: 1.21 × 0.9 = 1.089. 1.1 × 0.11 = 0.121. Form the ratio: 1.089 / 0.121 = 9 (since 0.121 × 9 = 1.089). Thus the expression is √9 = 3.

Verification / Alternative check:
Write in fractions: 1.21 = 121/100, 0.9 = 9/10, 1.1 = 11/10, 0.11 = 11/100. The ratio becomes √[(121/100 * 9/10) / (11/10 * 11/100)] = √[ (121*9*100) / (100*10*121) ] = √9 = 3.

Why Other Options Are Wrong:
2, 9, 11 do not result from the exact simplification of the given decimals.

Common Pitfalls:
Handling decimals without grouping under one radical often leads to arithmetic slips. Combine under a single square root to simplify cleanly.

Final Answer:
3