Dear community, I am trying to move a prefactor, inside a radical to simplify an expression. It works when the radical is comprised of one or two terms, but for three or more it does not seem to work anymore:

Simplify[a Sqrt[1 + b^2/a^2], a > 0]
Simplify[(a + b) Sqrt[1 + c^2/(a + b)^2], (a + b) > 0]
Simplify[(a + b + c) Sqrt[1 + d^2/(a + b + c)^2], (a + b + c) > 0]

Gives

Sqrt[a^2 + b^2]
Sqrt[a^2 + 2 a b + b^2 + c^2]
(a + b + c) Sqrt[1 + d^2/(a + b + c)^2]

How to obtain

Sqrt[ a^2 + 2 a b + b^2 + 2 a c + 2 b c + c^2 + d^2]

And, is it also possible to obtain

Sqrt[  (a + b + c)^2+d^2]