Correct Option: D

As per the given above question , we have
Let, x = 6 + √6 + √6 + √6 +........
On squaring both sides, we have
x² = 6 + √6 + √6 + √6 +........
⇒ x² = 6 + x
⇒ x² - x - 6 = 0
⇒ x² - 3x + 2x - 6 = 0
⇒ x( x - 3 ) + 2( x - 3 ) = 0
⇒ ( x - 3 ) ( x + 2 ) = 0
⇒ x = 3 and x ≠ −2 because numbers are positive.
Thus , correct answer will be 3 .