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9 years ago asked a question Rounding error in sqrt(2) in Sage

In the following code,

sage: floor(sqrt(2)*sqrt(2.)/2)==1
True
sage: (sqrt(2.)*sqrt(2.)/2)==1.0
False
sage: (sqrt(2.)*sqrt(2.)/2)
1.00000000000000
sage :((2^(1/2.))== sqrt(2.))
True
sage: (((2.^(1/2))* sqrt(2.)) == 2.)
False

why is there an approximation error?
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