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What is #x = sqrt(2sqrt(2sqrt(2sqrt(2...))))# ?

Answer 1

Isaiah Anthony

#x=2#

Given:

#x = sqrt(2sqrt(2sqrt(2...)))#

Square both sides to get:

#x^2 = 2sqrt(2sqrt(2sqrt(2...))) = 2x#

So either #x=0#, which it obviously is not, or we can divide both ends by #x# to get:

#x = 2#

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Answer 2

Ethan Adkins

The value of x in the equation x = sqrt(2sqrt(2sqrt(2sqrt(2...)))) is 2.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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