Equalizing radicals by squaring: Solve for ? if √(25/15625) = √(?/30625).

Introduction / Context:
When two square roots are equal, their radicands (nonnegative) must be equal. We simplify one side and equate the interior fractions to find the missing numerator.

Given Data / Assumptions:

• √(25/15625) = √(?/30625).
• All quantities are nonnegative.

Concept / Approach:
First simplify 25/15625. Then set the simplified fraction equal to ?/30625 and solve for the unknown numerator.

Step-by-Step Solution:

Verification / Alternative check:
Compute √(?/30625) with ? = 49: 49/30625 = 1/625; √(1/625) = 1/25, matching the left side.

Why Other Options Are Wrong:

• 2, 35, 1225, 625 do not produce the same radicand 1/625 on the right side.

Common Pitfalls:
Equating the square roots without equating the radicands, or forgetting to simplify 25/15625 first.

Final Answer:
49