Question

What is the square root of (14 + 6√5) ?
1. 3 + √5
2. 3 + 2√5
3. 5 + √3
4. 2 + √5

Answer 1

Correct Answer - Option 1 : 3 + √5

Given: 

(14 + 6√5)

Concept:

(a + b)² = a² + b² + 2ab

Calculation:

First we convert given equation into given concept form

⇒ 14 + 6√5 = 14 + (2 × 3 × √5)

⇒ 14 + 6√5 = 9 + 5 + (2 × 3 × √5)

⇒ 14 + 6√5 = (3)² + (√5)² + (2 × 3 × √5)

Now the given equation become in the form of given concept so,

⇒ a = 3, b = √5 

⇒ (3)2 + (√5)2 + (2 × 3 × √5) = (3 + √5)²

⇒ 14 + 6√5 = (3 + √5)²

Now square root of (14 + 6√5) is 

⇒ √(14 + 6√5) = √(3 + √5)²

⇒ √(14 + 6√5) = 3 + √5

∴ √(14 + 6√5) is 3 + √5