Square-root equation with an unknown addend: If √(75.24 + N) = 8.71, determine the value of N.

Introduction / Context:
We are reversing a square-root operation to recover the missing addend inside the radical. This is a standard technique in quantitative aptitude involving squaring both sides carefully.

Given Data / Assumptions:

• √(75.24 + N) = 8.71.
• All quantities are decimal reals.
• No approximation is required beyond exact decimal squaring.

Concept / Approach:
Square both sides to eliminate the square root, then isolate N. The arithmetic requires precise decimal squaring of 8.71.

Step-by-Step Solution:

Verification / Alternative check:
Check: 75.24 + 0.6241 = 75.8641 and √75.8641 = 8.71 exactly.

Why Other Options Are Wrong:

• 6.241 and 62.41 are off by factors of 10 or 100.
• “None of these” is incorrect because 0.6241 is listed.
• 0.06241 is a decimal-place error.

Common Pitfalls:
Mis-squaring 8.71 or mishandling decimal subtraction can lead to place-value mistakes.

Final Answer:
.6241