Simplify (1/√3 – 1/√2)²

JAMB Mathematics 2023 51 views

Simplify (1/√3 – 1/√2)²

  1. 5/6 – √6/3 ✓
  2. 5/6 + √6/3
  3. 5/6 – 2√6/3
  4. 5/6 + 2√6/3

Explanation

Step 1: Use the formula (a – b)² = a² – 2ab + b²
Here a = 1/√3 and b = 1/√2

Step 2: Calculate a²
a² = (1/√3)² = 1/3

Step 3: Calculate b²
b² = (1/√2)² = 1/2

Step 4: Calculate 2ab
2ab = 2 × (1/√3) × (1/√2) = 2/√6
Rationalize: 2/√6 × √6/√6 = 2√6/6 = √6/3

Step 5: Combine all terms
= 1/3 – √6/3 + 1/2
= 2/6 – √6/3 + 3/6
= 5/6 – √6/3

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