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For simplicity, let's take a four digit number 4096

Starting at the right, mark off the digits in pairs: 40'96

The highest number whose square does not exceed 40 is 6 so deduct its square from 40, leaving 4, now bring in the 96 making 496. 6 is the first digit of the solution

Add another 6 to the 6, making 12, but call it 120. Now find a number you can add to 120 and multiply that by your new number to make 496. This number is 4 which works out exactly so the square root of 4096 is 64.

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