Show me a method of calculation of square roots please.

Question

In traditional long division only so many remainders may drop down which forces rationals to repeat or terminate. Can you show me a method for calculation of square roots that is different  showing that it is possible for the decimal form of an irrational like the square root of 2 never to repeat periodically?

Answer 1

 

      1 .  4   1   4                     put down the number 2 and pairs of 0's for each digit in the answer

      ____________

   √ 2. 00 00 00 00            what number squared is less than or equal to 2 ? 1

                                         put it up and bring it down on the left

1     1                                multiply 1 times 1

   _____

2     1 00                          add 1+1=2 and put it down and on the left

24     96                           whatever you put above the first set of 0's you put next to 2________

    ______                        multiply 4 times 24

          4 00                      add 24+4=28 or 14+14=28

281     281

    _______

          119 00

282                                 4 goes up and 4 goes next to 282

2824  11296

continue repeating this procedure to get more digits

 

another example...

      2 . 6  4  5

     ______________

   √7. 00 00 00

2   4

   ___

    3 00

46 276

    ____

       24 00

524  2096

       _____

         304 00

5285  26425