Question

What is the value of ((square root 2 )^sqrt2) ^ sqrt2 ??

Very interesting. ...

$y = ({ ({ \sqrt{2} )}^{ \sqrt{2} } })^{ \sqrt{2} }$
What is the value of y?

Answer 1

heya sir!
here's your answer!

as mentioned in the QUESTION that the value of y is (square root 2 )^sqrt2) ^ sqrt2 .

the Answer will be 2
let me explain:-
= ((square root 2 )^sqrt2) ^ sqrt2

= (sqrt2)^2½^2½
(in this step we will multiply the last two sqrt2
hence the result will be :- 2

= [ sqrt2 multipled by sqrt2 will give 2 ]

hence the next step would be,

= sqrt2^2

if we do (sq.root of 2)²
Answer will be,

= 2

hence y= 2
Hope I'm clear and understandable:)

Answer 2

$= (( \sqrt{2} ) {}^{ \sqrt{2} } ) {} {}^{ \sqrt{2} }$

Here after multiplying the powers we get.

=(√2)^√2×√2
=(√2)^2
=2

Comment below for any doubt.