Find the number N such that (square root of N) divided by 19 equals 4; that is, sqrt(N) / 19 = 4. Determine the value of N.

Introduction / Context:
This item assesses comfort with undoing a square root relation presented in a fractional form. By isolating the square root term and then squaring both sides, we recover the original number. It is a straightforward arithmetic manipulation once the equation is read correctly.

Given Data / Assumptions:

• We are given sqrt(N) / 19 = 4.
• N is nonnegative since a real square root is implied.
• We need to find N.

Concept / Approach:
Multiply both sides by 19 to isolate sqrt(N), then square both sides to eliminate the square root. This yields N directly. Always check by substitution to avoid errors from misreading the original expression.

Step-by-Step Solution:

Verification / Alternative check:
Check: sqrt(5776) = 76 and 76 / 19 = 4. The original relation holds exactly.

Why Other Options Are Wrong:
76 is the square root, not N. 304 and 1296 do not satisfy the equation. 361 is 19^2, which would make sqrt(N) = 19, yielding 1 when divided by 19, not 4.

Common Pitfalls:
Confusing N with sqrt(N), or squaring 19 incorrectly. Some may multiply 4 * 19 and stop without squaring, which is incomplete.

Final Answer:
5776