IMO Its E
From 1
a^2+b^2=2
now a^=1/2 and b^2=3/2 satisfies this as well as a^2=b^2=1..not suffcient

From2
No new info its providing

hence both together also not sufficient.Can you please check the OA?

colakumarfanta wrote:Is Rectangle ABCD a square ?
1) The length of a diagonal is square root 2
2) angle between diagonal and side of the rectangle is 45 degrees
OA [spoiler]should be A ...right ?[/spoiler]

is 2) angle between diagonal and side of the rectangle ?
in that case the diagonal divides the rectangle into two isosceles triangle
and the two adjacent sides are equal
since it is a rectangel the opp sides are equal
therefore the rectangle is also a square.
Suff
1) the square of the diagonal is = 2
the sum of the square of the two adjacent sides should be = 2
if it was given that the sides have interger values than it is sufficient, otherwise not. So Insuff.
IMO B