  We study the real roots of the Yablonskii-Vorob'ev polynomials, which are
special polynomials used to represent rational solutions of the second
Painlev\'e equation. It has been conjectured that the number of real roots of
the nth Yablonskii-Vorob'ev polynomial equals [(n+1)/2]. We prove this
conjecture using an interlacing property between the roots of the
Yablonskii-Vorob'ev polynomials. Furthermore we determine precisely the number
of negative and the number of positive real roots of the nth
Yablonskii-Vorob'ev polynomial.
