Roots under sidewalk

Just wanted to thank those who posted in answer to my question about the roots under my sidewalk. I waited until I knew more, which I thought would be a couple days after you guys replied, but the sidewalk is a lot thicker and heavier than I expected. And I have to get a better fulcrum and a neighbor to help me.
Thank you all, and I plan to let you know how it all turns out.
P.S. I've been reading about root barriers, but it sounds like they weren't very common for private use 24 years ago, when this tree was planted. (At any rate, the first owner of the house didn't do it.) I'm going to try to push a spade down about 6 inches, next to the sidewalk, and push a scrap piece from vinyl siding into the slit. I figure six inches are better than nothing. And I found a second root lifting the next sidewalk square, though only a little bit now.
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