Square root equation with simple ratio: If √256 ÷ √x = 2, find the value of x.

Introduction / Context:
A quick manipulation of square roots and ratios. Converting square roots to base values and isolating the unknown is a frequent aptitude operation.

Given Data / Assumptions:
√256 / √x = 2.

Concept / Approach:
Use √a / √b = √(a/b). Alternatively, rewrite √256 = 16 and solve 16 / √x = 2 to find √x, then square to get x.

Step-by-Step Solution:
√256 = 16.16 / √x = 2 ⇒ √x = 8.x = 8^2 = 64.

Verification / Alternative check:
Substitute back: √256 / √64 = 16 / 8 = 2, which matches.

Why Other Options Are Wrong:
128, 256, 512, 1024 give √x values that do not produce the ratio 2 when plugged back.

Common Pitfalls:
Confusing 256 with 2^8 or miscomputing √256, or squaring 8 incorrectly.

Final Answer:
64