Simplify: $\sqrt{12} ( \sqrt{48} - \sqrt{3}$)

Analyze the question: We need to simplify √12(√48 − √3). The trick is to write each surd in its simplest form first.

Concept: √(a×b) = √a × √b, so we can pull out perfect squares.

Step 1: Simplify each surd

• √12 = √(4×3) = 2√3
• √48 = √(16×3) = 4√3
• √3 stays as √3

Step 2: Simplify the bracket √48 − √3 = 4√3 − √3 = 3√3

Step 3: Multiply √12 × 3√3 = 2√3 × 3√3 = 6 × (√3 × √3) = 6 × 3 = 18

Check by another method: √12 × √48 = √576 = 24 √12 × √3 = √36 = 6 24 − 6 = 18 ✓

Answer: A (18)

Tip: When you see surds, always reduce them to a common surd first (here, all became multiples of √3). Then like terms combine easily, and √3 × √3 = 3.