Simplify; $\sqrt{2}(\sqrt{6} + 2\sqrt{2}) - 2\sqrt{3}$

Analyze the question: We need to expand the bracket, simplify the surds, and combine like terms.

Concept: Use the distributive law and the rule √a × √b = √(ab).

Solution:

√2(√6 + 2√2) − 2√3

Step 1: Expand the bracket = (√2 × √6) + (√2 × 2√2) − 2√3

Step 2: Multiply each term

• √2 × √6 = √12 = √(4×3) = 2√3
• √2 × 2√2 = 2 × (√2 × √2) = 2 × 2 = 4

Step 3: Substitute back = 2√3 + 4 − 2√3

Step 4: Collect like terms The 2√3 and −2√3 cancel out, leaving:

= 4

Answer: The correct option is A. 4.

Tip: In surd questions, always simplify each product first (like √12 = 2√3). Terms that look different often turn out to be like terms that cancel. Remember √a × √a = a.