Let x be equal to the given expression Squareroot(2+Sqrt
(2+Sqrt(2.............
x=sqrt(2+x)
squaring both sides we get
xsquare=2+x
or
xsquare-x-2=0
which is nothing but a quadratic equation
after solving this you ll get x to be 1 or -2[rejected 
because sqrt of some no. cant be negative]
so the answer is 1