Square roots

Do it on a calculator! If you don't want to use a calculator, then make an educated guess and follow this procedure: Let us take sqrt of 50. what number multiplied by itself gives you a number close to 50? Obviously it would be 7, because 7 X 7=49. Once you guess a number, then you divide 50/7=7.142857 + 7=14.142857/2=7.0714285. Now, this is your next approximation. Next, you go back to dividing 50 by this new number, thus: 50/7.0714265=7.07070707 + 7.0714265=14.142134/2=7.071067.......and so on. If you take this last number we got, 7.071067 and multiply it by itself(or square it, which is the same thing), this is the answer that you will get:

7.071067^2=49.99999......etc. So, you can see how close to 50 you are. This method was discovered by Isaac Newton. But it's cumbersome and labourious. It will take you a lot of time to do it manually. I strongly recommend that you use a clculator. You can buy one for $5. Good luck.