Simplify (√3 − 1)².

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