The value of ` (sqrt(3+2sqrt2)+sqrt(3-2sqrt2))^(2^(9))` is ________.

Answer

6

Explanation

`3+2sqrt2=(sqrt2+1)^(2) and 3-2sqrt2=(sqrt2-1)^(2)`
` rArr log_((sqrt(3+2sqrt2)+sqrt(3-2sqrt2)))2^(9)`
` = 1/(log_(2^(9))((sqrt2+1)+(sqrt2-1)))`
` = 1/(log_(2^(9))2^(3//2))`
` = 9/(3//2)=6`