simplification with exponents

[ribrdb]

I would expect these to simplify to zero:

simplify(sqrt(2x)-(sqrt(2)*x^(1/2)))
(2*x)^(1/2)-2^(1/2)*x^(1/2)

simplify(sqrt(2e)-(sqrt(2)*e^(1/2)))
(2*e)^(1/2)-2^(1/2)*exp(1/2)

[soegaard]

I would expect these to simplify to zero:
simplify(sqrt(2x)-(sqrt(2)*x^(1/2)))

I agree.

The rule sqrt(xy)=sqrt(x)sqrt(y) can't be used in general, when x and y are complex.
But here, we know that x is a positive, real number.