Palm roots donot expand with age like hardwood trees 6 feet should be good.

You may want to post this in the Palms & Cycads Forum. There will be many more folks knowledgeable about palm roots there. See link below. I would also post it in the Florida Gardening Forum for the mere fact that so many Floridians have both palm trees and pools. You will probably get lots of responses on both of those forums.

Carol

Here is a link that might be useful: Palms & Cycads

Been doing Mexican palms near pools for 18 years. I would say 7 is safe. Planting the palms too far from pool looses its look and I believe is not needed to be so far away. Roots grow mostly downward and across approx. 7 feet. so that is 3'.5" - 4' feet in each direction from center of trunk, giving extra few feet of room/space between pool wall and roots. Water Mexican palm tree with more water to get it close to desired height, then cut back water and will grow much slower.

Rick