Square-root based division: Find the value that should replace the question mark so that ? / √2.25 = 550.
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A825
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B82.5
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C3666.66
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D2
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E550
Answer
Correct Answer: 825
Explanation
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:
Compute √2.25. Since 1.5 * 1.5 = 2.25, √2.25 = 1.5.Given ? / 1.5 = 550.Multiply both sides by 1.5: ? = 550 * 1.5 = 825.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