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:
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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