Evaluate the radical quotient: What is √4375 / √7 equal to?

Difficulty: Easy

Correct Answer: 25

Explanation:


Introduction / Context:
When dividing square roots, combine them into a single radical to simplify. Look for perfect-square simplifications.


Given Data / Assumptions:
Expression: √4375 / √7.


Concept / Approach:
Use √a / √b = √(a/b). If the fraction simplifies to a perfect square, the square root becomes an integer.


Step-by-Step Solution:

√4375 / √7 = √(4375 / 7)Since 7 * 625 = 4375, the fraction equals 625√625 = 25


Verification / Alternative check:
4375 = 7 * 625 confirms the simplification; 625 is 25^2.


Why Other Options Are Wrong:
24.75 and 27.25 are near-by distractors; 35 and 20 are unrelated integers not supported by the exact simplification.


Common Pitfalls:
Rationalizing or approximating too early; here, exact simplification is cleaner.


Final Answer:
25

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