Simplify (√3 − 1)<sup>2</sup>.
Aptitude
Square Root and Cube Root
Difficulty: Easy
Choose an option
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A4 − 2√3
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B2√3 − 1
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C3 − √3
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D√3
Answer
Correct Answer: 4 − 2√3
Explanation
Problem restatementExpand and simplify the binomial square (√3 − 1)2.
Concept/ApproachUse (a − b)2 = a2 − 2ab + b2.
Step-by-step calculation (√3 − 1)2 = (√3)2 − 2(√3)(1) + 12 = 3 − 2√3 + 1 = 4 − 2√3
Verification/AlternativeNumeric check: √3 ≈ 1.732 ⇒ (1.732 − 1)2 ≈ 0.7322 ≈ 0.536; 4 − 2√3 ≈ 4 − 3.464 ≈ 0.536 (matches).
Final Answer4 − 2√3