This is a jukugo word, which usually means on'yomi readings from the kanji. If you know the readings of your kanji you'll know how to read this as well. 大 uses the だい reading because if you try to put the whole thing in your mouth at once you'll probably end up choking and dying.
I've tried to grow daikon once, but they all withered and died.
My family hangs up stockings and dried Japanese radishes for the Christmas season.
Hey, check it out! These are really nice Japanese radishes. Do you want one of these too?