Simplify: (12 6 3)+

Question

Simplify: (12 6 3)+

1. A. 2 + 3
2. B. 3 + 3 (Correct answer)
3. C. 3 + 2 3
4. D. 3 + 9

Correct Answer

Option B — 3 + 3

Detailed Solution & Explanation

The correct answer is 3 + 3.

Key Points

• Recognise 12 + 6√3 as a perfect square.
• Write it as 3² + (√3)² + 2·3·√3 = 9 + 3 + 6√3 = 12 + 6√3, which is (3 + √3)².
• Therefore √(12 + 6√3) = 3 + √3 (positive root).
• For surds of the form √(a + b√c), try to express the inside as (√x + √y)² by matching the cross term 2√(xy) to b√c; here 6√3 = 2·3·√3 gives x = 9, y = 3.