# The value of the expression √(6+√(6+√(6+…..+ ))) up to ∞ is :

**Answer: (1) 3 **

**Explanation:-**

√(6+√(6+√(6+…..+ )))

Let X = √(6+√(6+…..+ ))

Then, X = √(6+ X)

Square root on both side,

X² = 6 + X

X² – X – 6 = 0

X² – 3 X + 2 X – 6 = 0

X (X – 3) + 2 (X – 3) = 0

(X + 2) (X – 3) = 0

X = 3, – 2

But – 2 < 0 therefore, X = 3.

Then, the value of √(6+√(6+√(6+…..+ ))) is 3.

Hence, the correct answer is option (1) 3.