It is well known since Noether that the gonality of a smooth curve
C
⊂
P
2
{C\subset \mathbb {P}^2}
of degree
d
≥
4
d\geq 4
is
d
−
1
d-1
. Given a
k
k
-dimensional complex projective variety
X
X
, the most natural extension of gonality is probably the degree of irrationality, that is, the minimum degree of a dominant rational map
X
⇢
P
k
{X\dashrightarrow \mathbb {P}^k}
. In this paper we are aimed at extending the assertion on plane curves to smooth hypersurfaces in
P
n
\mathbb {P}^n
in terms of degree of irrationality. We prove that both surfaces in
P
3
\mathbb {P}^3
and threefolds in
P
4
\mathbb {P}^4
of sufficiently large degree
d
d
have degree of irrationality
d
−
1
d-1
, except for finitely many cases we classify, whose degree of irrationality is
d
−
2
d-2
. To this aim we use Mumford’s technique of induced differentials and we shift the problem to study first order congruences of lines of
P
n
\mathbb {P}^n
. In particular, we also slightly improve the description of such congruences in
P
4
\mathbb {P}^4
and we provide a bound on the degree of irrationality of hypersurfaces of arbitrary dimension.