Sum of a cube and a square equals 4425: If (14)^3 is added to the square of a number, the result is 4425. Find the number.

Introduction / Context:
This problem mixes perfect cubes and perfect squares, requiring inverse operations to isolate the unknown square.

Given Data / Assumptions:
14^3 + n^2 = 4425.

Concept / Approach:
Compute 14^3 first, subtract from 4425 to get n^2, then take the square root to get n.

Step-by-Step Solution:
14^3 = 2744.n^2 = 4425 − 2744 = 1681.n = √1681 = 41.

Verification / Alternative check:
41^2 = 1681. Adding 2744 returns 4425.

Why Other Options Are Wrong:
43 is not the number (though 1849 = 43^2 is a distractor). 1681 and 1849 are square values, not the number n itself.

Common Pitfalls:
Reporting n^2 instead of n, or miscomputing 14^3.

Final Answer:
41