解:
(1) $a$不是有理数。
理由:$\because π a^2=5π,$
$\therefore a^2=5。$
$\because a>0,$且找不到平方后等于5的有理数,
$\therefore a$是无理数,不是有理数。
(2) $\because 2^2<5<3^2,$
$\therefore 2<a<3。$
$\because 2.2^2=4.84,$$2.3^2=5.29,$
$\therefore 2.2<a<2.3。$
$\because 2.23^2=4.9729,$$2.24^2=5.0176,$
$\therefore 2.23<a<2.24,$
$\therefore a\approx2.2。$