© T Madas

These days no one has the need to manually compute square roots. The algorithm which follows has been put to oblivion by the modern calculator, I am pleased to say! Nevertheless it is worth showing the algorithm; it is very impressive after all

x Find the square root of Split the number in digit pairs starting from the right Find the square root of the first pair from the left, without going over 8 is the first digit of the answer Subtract 8 2 from the first pair of digits Bring down the next pair of digits Double your answer of 8 into 16 Find a digit to place at the end of 16 and at the same time multiply the newly created number by the same digit, trying to make 698 without going over 4 is the next digit 4

© T Madas x x Find the square root of Subtract 656 from the last remainder Bring down the next pair of digits Double your answer of 84 into 168 Find a digit to place at the end of 168 and at the same time multiply the newly created number by that digit, trying to make up 4206 without going over 2 is the next digit 2

© T Madas x x x Find the square root of Subtract 3364 from the last remainder Bring down the next pair of digits Double your answer of 842 into 1684 Find a digit to place at the end of 1684 and at the same time multiply the newly created number by that digit, trying to make up without going over 5 is the next digit Subtract from the last remainder to give zero, terminating the algorithm 0

© T Madas

x 6x Find the square root of Split the number in digit pairs starting from the right Find the square root of the first pair from the left, without going over 2 is the first digit of the answer Subtract 2 2 from the first pair of digits Bring down the next pair of digits Double your answer of 2 into 4 Find a digit to place at the end of 4 and at the same time multiply the newly created number by the same digit, trying to make 303 without going over 6 is the next digit 6

© T Madas x 6x Find the square root of x 5x Subtract 276 from the last remainder Bring down the next pair of digits Double your answer of 26 into 52 Find a digit to place at the end of 52 and at the same time multiply the newly created number by that digit, trying to make up 2784without going over 5 is the next digit 5

© T Madas x 6x Find the square root of x 5x x 3x Subtract 2625 from the last remainder Bring down the next pair of digits Double your answer of 265 into 530 Find a digit to place at the end of 530 and at the same time multiply the newly created number by that digit, trying to make up without going over 3 is the next digit Subtract from the last remainder to give zero, terminating the algorithm 0

© T Madas