Thank you! This is the way I learned it, but with the use of hand-held calculators and enough time, I managed to forget it. When my son was getting to the age when he should have learned this, I asked his math teacher who stared at me like I was crazy and told me you CANNOT do a square root by hand. Since that day it has bothered me a lot, I knew I used to do square roots by hand but I asked a number of high school and college instructors and they all acted like I was crazy. Thank you for posting this, you made my day!
I wonder how all those papyrus and cuneiform tables of square and cube roots compiled four thousand years ago were created? Must have been ancient aliens, it's the only thing that makes sense.