What is the value of (√(2) + √(3))^2?
Correct Answer: 5 + 2√(6)
- Step 1: Start with the expression (√(2) + √(3))^2.
- Step 2: Use the formula (a + b)^2 = a^2 + 2ab + b^2, where a = √(2) and b = √(3).
- Step 3: Calculate a^2: (√(2))^2 = 2.
- Step 4: Calculate b^2: (√(3))^2 = 3.
- Step 5: Calculate 2ab: 2 * (√(2)) * (√(3)) = 2√(6).
- Step 6: Combine all parts: 2 + 3 + 2√(6).
- Step 7: Simplify the expression: 2 + 3 = 5, so the final result is 5 + 2√(6).
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