  In this paper questions of the width in verbal subgroups of $A_n$ is
considered. Verbal width by set of squares of alternating group is found, it is
happened equals to 2. The criterion of squareness in $A_n$ is presented. The
necessary and sufficient conditions when an element of alternating group can be
presented as a squares of one element are also found by us. Some necessary
conditions to an element $g\in A_n$ being the square in $A_n$ are investigated.
