Question

what will be the value of
$\sqrt{6 + \sqrt{6 + \sqrt{6....} } }$
​

Answer 1

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Step-by-step explanation:

Hi there!

Given : x = √6 + √6 + √6 +... ---(i)

Then,

x = √6 + x --- From Eqn. (i)

On squaring both sides,

⇒ x² = 6 + x

⇒ x² - x - 6 = 0

⇒ x² - 3x + 2x - 6 = 0

⇒ x(x-3) + 2(x-3) = 0

⇒ x = 3 Or x = -2

But x is a natural number.

∴ x = 3

[ Thank you! for asking the question. ]

Hope it helps!