by MrAlgebra on Tue May 24, 2011 7:44 pm
I don't mean to bump an old thread, but I would start off by realizing that the ones digit of the square root has to be 3 since it ends in 9. Look at the following: 0² = 0, 1² = 1, 2² = 4, 3² = 9, 4² = 16 (ends in 6), 5² = 25 (ends in 5), 6² = 36 (ends in 6), 7² = 49 (ends in 9), 8² = 64 (ends in 4), and 9² = 81 (ends in 1).
Then I would see that the square root has 3 digits because 100² = 10000 and 1000² = 1000000, and 29929 is somewhere in the middle. I'd see that 200² = 40000, so our answer is between 100 and 200. To narrow it down a bit more, we can find that 160² = 25600, we know it's between 160 and 200. There are only a few possibilities to check: 169, 179, 189, 199.
I hope this helps if anyone looks for advice on a similar problem.