Nested Radicals

Algebra Level 3

$2^{\sqrt{2^{\sqrt{2^{\sqrt{2^{\cdots}}}}}}}$
Find the value of the expression above.

2 4 1 0

3 solutions

Sravanth C.
Mar 9, 2015

I think this is more better,

First solve $\sqrt { 2\sqrt { 2\sqrt { 2\sqrt { 2... } } } }$

$\sqrt { 2\sqrt { 2\sqrt { 2\sqrt { 2... } } } } =\quad x$

$\sqrt { 2x } =\quad x$

$2x =x^{2}$

or, $x = 2$

Now, put two as the power,

therefore, $2^{ 2 }\quad =\quad 4$

Thomas James Bautista
Feb 27, 2015

$2^{\sqrt{2^{\sqrt{2^{\sqrt{2^{...}}}}}}}=x$

$2^{\sqrt{x}}=x$

Trial and error...

$x=4$

Put $x = 16$

Even then the equation is satisfied.

Sakanksha Deo - 6 years, 3 months ago

Never thought about that Well, there isn't a 16 in the choices, so 4 it is :D

Thomas James Bautista - 6 years, 3 months ago

I think you are right at your place. But this issue should be looked forward by the creater of this problem....isn't it !

Sakanksha Deo - 6 years, 3 months ago

Arman Hemel
Mar 6, 2015

hoy nai :-P result hoise but solution is wrong, uporer solution thik ache

Sanjoy Roy - 6 years, 2 months ago