By now, I could chop an onion in my sleep: Slice it in half, trim off the stem and root, peel, and slice away. In all my years of onion prep, it never occurred to me to shake things up, but skipping just one of those steps — removing the root — has changed my heavily onion-based repertoire for the better.
The hardest part of dicing an onion is keeping the slippery layers from splaying out at weird angles, ruining the uniformity of the dice and creating a potentially dangerous cutting surface. If this is something you struggle with, keeping the root intact is super helpful. It holds the layers together as you cut them and gives you a convenient little handle to grip, both of which keep everything nice and stable.
To try it out yourself, just halve your onion through the root and lop off the stem side like normal, leaving the root as-is. Peel off the skin, then chop, slice, or dice your onion however. When you make it down to the root end, don’t you dare throw it away — slice it off and save it for stock instead.