Solve for the radicand from a quotient: Find ? such that 1872 / √? = 234.

Introduction / Context:
This problem asks for the number whose square root appears in a denominator. It reduces to isolating the square root and then squaring to retrieve the radicand.

Given Data / Assumptions:

• Equation: 1872 / √? = 234.
• All values are positive reals.

Concept / Approach:
Isolate √? by dividing 1872 by 234. Once √? is known, square it to find ?.

Step-by-Step Solution:

Verification / Alternative check:
Check: 1872 / √64 = 1872 / 8 = 234. Works exactly.

Why Other Options Are Wrong:

• 324, 256 would yield square roots 18 or 16, not 8.
• 8 is √?, not ? itself.
• 36 gives √? = 6, which is incorrect here.

Common Pitfalls:
Stopping at √? = 8 and selecting 8 as the answer. The question asks for ?, not its square root.

Final Answer:
64