Simplify the radical expression: sqrt(75) - sqrt(27) + sqrt(12).
Answer and explanation
Correct answer: B. 4*sqrt(3)
- Step 1: Express each radicand in terms of perfect squares and 3:
- Step 2: sqrt(75) = sqrt(25 3) = 5sqrt(3); sqrt(27) = sqrt(9 3) = 3sqrt(3); sqrt(12) = sqrt(4 3) = 2sqrt(3).
- Step 3: Combine coefficients: (5 - 3 + 2)sqrt(3) = 4sqrt(3).
Answer
4*sqrt(3).
Why not the others: Option 2sqrt(3) subtracts the last term instead of adding. Option 6sqrt(3) adds all three terms without subtracting sqrt(27). Option 3*sqrt(3) miscalculates 5 - 3 + 2.
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