Sum of square roots with scaled decimals: Given √15625 = 125, evaluate √15625 + √156.25 + √1.5625.

Introduction / Context:We combine square roots of numbers that are decimal scalings of one another. Recognizing powers of 10 under square roots simplifies computation.

Given Data / Assumptions:

• √15625 = 125 (given).
• 156.25 = 15625 / 100.
• 1.5625 = 15625 / 10000.

Concept / Approach:Use √(A/100) = √A / 10 and √(A/10000) = √A / 100 for positive A. Apply to A = 15625.

Step-by-Step Solution:

Verification / Alternative check:Compute squares: 12.5^2 = 156.25 and 1.25^2 = 1.5625, confirming the decomposition.

Why Other Options Are Wrong:

• Values like 1.3875 and 13.875 drop decimal places incorrectly.
• 156.25 confuses a square root with the original radicand.

Common Pitfalls:Forgetting to divide by 10 or 100 when taking square roots of numbers reduced by factors of 100 or 10000.

Final Answer:138.75