Simplify $3\sqrt{12} + 10\sqrt{3} - \frac{6}{\sqrt{3}}$

Step 1: Analyze the question We need to simplify each term so that every term is a multiple of √3, then combine them.

Step 2: Concept

• Simplify surds by pulling out perfect squares: √12 = √(4×3) = 2√3
• Rationalize the denominator: a/√3 = a√3/3

Step 3: Solution

• 3√12 = 3 × 2√3 = 6√3
• 10√3 stays as 10√3
• 6/√3 = (6×√3)/(√3×√3) = 6√3/3 = 2√3

Combine: 6√3 + 10√3 − 2√3 = (6 + 10 − 2)√3 = 14√3

Step 4: Answer The result is 14√3, which is option C.

Tip: Always reduce each surd to its simplest form first (and rationalize any denominators). Then you can add or subtract like terms just as you would with ordinary algebraic terms like 6x + 10x − 2x.