Square roots

My daily rag prints a number of puzzles each day, including three crosswords and two sudokus. I usually try to complete the cryptic crossword (the so-called toughie is beyond me and I leave the quickie for Madam) and the sudokus. One puzzle I have never managed to get my mind round is the Mind Gym. This consists of three mental arithmetic puzzles of increasing difficulty and the object is to try to complete each one in under 30 seconds. Each puzzle gives a number, followed by a series of instructions. For example, 3, then x25, then -15, then x2/3, and so on. The first (and simplest) is usually within my power, but the third is generally quite beyond me. Take today's, for example. It started by asking for the square root of 784. I haven't the foggiest idea how to work out the square root of any number quickly, but realised that the answer must be less than 30 as 30 x 30 is 900. And as 20 x 20 is 400, the answer probably lies in the upper 20s. It actually needs to end in an 8 (assuming that we are talking whole numbers and not fractions), so 28 seemed a pretty safe bet.

This led me to search the internet for simple ways of working out square roots — but it seems that there aren't any! They all involve guess work and estimation. I shall just have to give up on the third puzzle when square roots are involved.