Difficulty: Easy
Correct Answer: 1/(2√3)
Explanation:
Introduction / Context:This problem involves subtracting two simple radicals with fractional arguments. Express each in simplified radical form, then subtract using a common denominator.
Given Data / Assumptions:Expression: √(4/3) − √(3/4).
Concept / Approach:√(4/3) = 2/√3 and √(3/4) = √3/2. Subtract the two by writing over a common denominator.
Step-by-Step Solution:
√(4/3) = 2/√3√(3/4) = √3/2Difference = 2/√3 − √3/2Common denominator = 2√3 ⇒ (4 − 3) / (2√3) = 1/(2√3)Verification / Alternative check:Approximate numerically: √(4/3) ≈ 1.1547; √(3/4) ≈ 0.8660; difference ≈ 0.2887; 1/(2√3) ≈ 1/(2 * 1.732) ≈ 0.2887.
Why Other Options Are Wrong:The negative option reverses order; 1 and 2√3 are far off; 0 implies equality which is false.
Common Pitfalls:Subtracting numerators or denominators directly without a common denominator; forgetting to rationalize is fine here since the exact form 1/(2√3) is acceptable.
Final Answer:1/(2√3)
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