Radical of a decimal ratio: Evaluate √(0.289 / 0.00121) and give the exact simplified value.

Introduction / Context:
Even when decimals look messy, converting to fractional form can expose perfect squares. The goal is to simplify the ratio inside the square root completely before taking the root.

Given Data / Assumptions:

• Compute √(0.289 / 0.00121).
• Decimals are exact and correspond to familiar squares (289 and 121) after scaling.

Concept / Approach:
Write decimals as fractions, reduce the ratio, and then take the square root of numerator and denominator separately.

Step-by-Step Solution:

Verification / Alternative check:
Compute (170/11)^2 = 28900/121 = (0.289)/(0.00121), confirming exactness.

Why Other Options Are Wrong:

• 1.7 and 17/10 equal 1.7, far too small.
• 17/11 ≈ 1.545, also too small.
• Exact answer is a rational number 170/11.

Common Pitfalls:
Taking square roots of decimals directly without fraction conversion; misplacing decimal points in scaling.

Final Answer:
170/11