Square-root based division: Find the value that should replace the question mark so that ? / √2.25 = 550.

Introduction / Context:
This is a direct square-root and proportion problem. We are given a simple equation involving a square root in the denominator and asked to find the missing numerator so the equality holds.

Given Data / Assumptions:

• Equation: ? / √2.25 = 550.
• All numbers are real and positive.
• Arithmetic uses standard real-number operations.

Concept / Approach:
First, evaluate the square root. Then isolate the unknown by multiplying both sides by that square-root value. This is a single-step linear manipulation once the square root is known.

Step-by-Step Solution:

Verification / Alternative check:
Substitute back: 825 / 1.5 = 550, which confirms the result exactly.

Why Other Options Are Wrong:

• 82.5 and 2 are far too small to yield 550 when divided by 1.5.
• 3666.66 would give a value much larger than 550 when divided by 1.5.
• 550 would imply √2.25 = 1, which is incorrect.

Common Pitfalls:
Forgetting that √2.25 = 1.5, not 1. Also, avoid rounding early—this problem is exact with 1.5.

Final Answer:
825