Evaluate the missing value: 4050 divided by sqrt(N) equals 450. That is, 4050 / sqrt(N) = 450. Find N.

Introduction / Context:
This question involves solving a simple equation with a square root in the denominator. The strategy is to isolate the square root, compute its value, and then square to obtain N. It checks manipulation of radicals and proportional reasoning.

Given Data / Assumptions:

• Equation: 4050 / sqrt(N) = 450.
• N is positive to make sqrt(N) real and nonzero.
• We seek N.

Concept / Approach:
Cross-multiply to isolate sqrt(N). Once sqrt(N) is expressed numerically, square to find N. Verify by substituting back to the original equation to ensure no arithmetic slip occurred.

Step-by-Step Solution:

Verification / Alternative check:
Substitute: 4050 / sqrt(81) = 4050 / 9 = 450. This matches the given relation.

Why Other Options Are Wrong:
49, 100, 9, and 36 produce sqrt(N) values that do not yield 450 when dividing 4050.

Common Pitfalls:
Computing 4050 / 450 incorrectly or forgetting to square 9 to get N. Mixing up whether the square root is in the numerator or denominator can also cause errors.

Final Answer:
81