Question

$\sqrt{2 + \sqrt{2 + \sqrt{2 + \sqrt{2 + ..........} } } } =$
?

Answer 1

Consider RHS as x
Then

x = √(x +2)

x² = x + 2

x² - x - 2 = 0

x² - 2x + x - 2 = 0

x(x - 2) +1(x - 2) = 0

(x - 2)(x + 1) = 0

So, x can be 2, -1

As the value of a square root is positive so your answer is 2.

Thank you.