Clarify grouping and evaluate: Compute √(0.16 / 0.4) and choose the correct decimal approximation.

Introduction / Context:The original text can be ambiguous; consistent with the options, interpret it as √(0.16 / 0.4). We simplify the fraction first, then take the square root and compare to the listed choices.

Given Data / Assumptions:

• Evaluate √(0.16 / 0.4).
• Use principal (positive) square roots.

Concept / Approach:Simplify the ratio inside the root: 0.16 / 0.4 = 16/40 = 2/5 = 0.4. Then take √0.4 and express as a decimal or simple surd if needed.

Step-by-Step Solution:

Verification / Alternative check:Square 0.63 ≈ 0.3969, close to 0.4; using exact (√10)/5 squared is exactly 0.4.

Why Other Options Are Wrong:

• 0.2 and 0.02 are too small.
• 2√5/5 ≈ 0.894 is too large.
• 1 is the value of √0.16/0.4 if mis-grouped; with correct grouping the value is ≈ 0.632.

Common Pitfalls:Ignoring parentheses and computing (√0.16)/0.4 = 1; the intended grouped form avoids this ambiguity.

Final Answer:0.63