她睡着了。 tā shuìzháo le. - She has fallen asleep.
她睡不着。tā shuìbùzháo. – She can't fall asleep.
But beware, this character is most commonly pronounced 着 zhe, and indicates a continuing action or state. It is often paired with 呢 ne:
他睡着呢。 tā shuìzhe ne. – She is sleeping.