A father comes back home from a long journey. He addresses his children complimenting the two of them for having grown up so much. Will he say: "Look how you've grown up both of you!" or rather "Look how you've grown up THE both of you!" By the way, is it "how you've grown up" or "how you're grown up"
If Father comes from Manchester he may well say 'the both of you'. 'The both' is a regional variation of 'both', common e.g. in the North West of England, and heard in the Morrissey song There Is A Light That Never Goes Out:
And if a ten-ton truck
Kills the both of us
To die by your side
Well, the pleasure - the privilege is mine
In formal writing or speech, avoid 'the both'.