I think both "around" and "about" deliver the similar meaning of approximation, but why does he say "around about" together in a row?
Yes, you are correct. "Around" and "about" both deliver a similar meaning of approximation, so "around about" is actually superfluous and unnecessary. The speaker only needs to have used one of these words to deliver his message. Ex: It's about 20 degrees Celsius today. Ex: It's around 20 degrees Celsius today.
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