Sum of two decimal square roots: Evaluate √0.0009 + √0.01 and select the correct value.

Introduction / Context:Addition of square roots of small decimals requires careful decimal handling. Each root is easy, but the sum must be computed exactly and compared to the options.

Given Data / Assumptions:

• Compute √0.0009 and √0.01 separately.
• Add the two results exactly.

Concept / Approach:Use √(a/10^n) = √a / 10^(n/2) when n is even; here both decimals are perfect squares in decimal form.

Step-by-Step Solution:

Verification / Alternative check:Square 0.03 to 0.0009 and 0.1 to 0.01 to confirm individual roots; then add.

Why Other Options Are Wrong:

• 3 and 1/3 are orders of magnitude off.
• 0.3 is too large; 0.13 is not listed as a distinct selectable value except via “None of these.”

Common Pitfalls:Confusing 0.0009 with 0.009 or misplacing decimal points when adding.

Final Answer:None of these