Simplify the product of radicals: (112/√196) × (√576/12) × (√256/8) = ?

Introduction / Context:Products of simple radical fractions are common in aptitude tests. The idea is to simplify each fraction individually using perfect squares and then multiply the results.

Given Data / Assumptions:The middle term uses √576 (a perfect square), ensuring clean simplification (576 = 24^2). We proceed assuming perfect-square radicals for tidy arithmetic.

Concept / Approach:Simplify each factor: 112/√196, √576/12, and √256/8. Replace square roots of perfect squares with integers (√196 = 14, √576 = 24, √256 = 16). Then multiply the simplified numbers.

Step-by-Step Solution:

Verification / Alternative check:Multiply numerators and denominators under one radical form is unnecessary here; direct simplification is fastest and exact.

Why Other Options Are Wrong:8, 12, 16, 24 arise from partially simplifying one or two terms but not all three correctly.

Common Pitfalls:Forgetting that √(a^2) = a for nonnegative a; miscomputing √576 or √196. Always check that the inner numbers are perfect squares.

Final Answer:32