Phrasal verbs can be separable or inseparable. To take off, meaning to rise into the air, is inseparable; the two words take and off must remain together to have this meaning. If they are separated as in he took it off, then the meaning is quite different (here: removed).
There are several dictionaries available for phrasal verbs and it is well worth owning one.
Also, a word of warning. Even when you think you know what a phrasal verb means, you may not use it appropriately.
Your example to put around reminded me of a class where I was teaching phrasal verbs. To put around (separable) is a phrasal verb. It means to spread a rumour; to imply; to suggest. But it has other - dangerous - meanings too:
A - She's been putting it around that he's leaving.
B - He's leaving?
A - Yes, she's been putting it around.
This is where the teacher tears his hair out. The last usage is inappropriate but the learner probably won't realise it. Only native speakers are likely to hear the innuendo. So another important factor with phrasal verbs is they cannot be left hanging. They really are a minefield for learners.