Sage cannot simplify expressions with radical functions?

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Sage cannot seem to simplify symbolic expressions containing radical functions, even if I specify the domain and use assumptions:

var('x', domain='positive')
assume(x>1)
bool(sqrt(x-1)>0) # True
bool(sqrt((x-1)^3)-(x-1)*sqrt(x-1)==0) #True
# not true even with x>1 assumption?
bool(sqrt(x^3-x^2)-x*sqrt(x-1)==0) #False

I know there is the simplify_chain_real() function that can simplify sqrt(x^3-x^2) to sqrt(x-1)*x, but shouldn't the bool() function force a simplification? And why the behavior is different (and correct) for bool(sqrt((x-1)^3)-(x-1)*sqrt(x-1)==0)?

Thanks