The object of this paper is to examine some radical properties of quadratic Jordan algebras and to show that under certain conditions,
R
(
B
)
=
B
∩
R
(
J
)
R(\mathfrak {B}) = \mathfrak {B} \cap R(\mathfrak {J})
where
B
\mathfrak {B}
is an ideal of a quadratic Jordan algebra
J
,
R
(
B
)
\mathfrak {J},R(\mathfrak {B})
is the radical of
B
\mathfrak {B}
, and
R
(
J
)
R(\mathfrak {J})
is the radical of
J
\mathfrak {J}
.