Difficulty: Medium
Correct Answer: 32
Explanation:
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
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