text: how do you work out the square root of a number without a calculator? its been buging me trial and error.  eg. square root of 52. it's between 7^2 and 8^2. so try 7.5^2 = 56.25 now try between 7^2 and 7.5^2, so try 7.25^2... and so on. eventually you'll come close.