Question

How do you prove that `(1/2)sqrt(2+sqrt(2+sqrt 2))=sqrt((1+sqrt((1+1/sqrt 2)/2)) /2)`?

Answer 1

Please see below.

Explanation:

`(1/2)sqrt(2+sqrt(2+sqrt2))`

= `sqrt((2+sqrt(2+sqrt2))/4)`

= `sqrt((1+sqrt((2+sqrt2))/2)/2)`

= `sqrt((1+sqrt((2+sqrt2)/4))/2)`

= `sqrt((1+sqrt((1+sqrt(2/4))/2))/2)`

= `sqrt((1+sqrt((1+sqrt(1/2))/2))/2)`