Simplify the expression involving surds completely: (√75 - √12) / √27.
Answer and explanation
Correct answer: B. 1
- Step 1: Simplify each radical: √75 = √(25 × 3) = 5√3; √12 = √(4 × 3) = 2√3; √27 = √(9 × 3) = 3√3. Step 2. Substitute into numerator: 5√3 - 2√3 = 3√3. Step 3. Divide: 3√3 / 3√3 = 1. Answer: 1. Why not the others: √3 leaves an uncancelled radical; 2 and 3 result from improper subtraction of coefficients.
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