Equalizing radicals by squaring: Solve for ? if √(25/15625) = √(?/30625).
Aptitude
Square Root and Cube Root
Difficulty: Easy
Choose an option
-
A2
-
B35
-
C49
-
D1225
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E625
Answer
Correct Answer: 49
Explanation
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:
25/15625 = 1/625 (divide numerator and denominator by 25).So √(25/15625) = √(1/625) = 1/25.Given equality of square roots ⇒ ?/30625 = 1/625.Cross-multiply: ? = 30625 / 625 = 49.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