1. © T Madas

2. 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

3. 70980625 64164 x 4 698 656 8 Find the square root of 70980625 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

4. © T Madas 70980625 64164 x 4 698 656 42 1682 x 2 3364 06 48 Find the square root of 70980625 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

5. © T Madas 70980625 64164 x 4 698 656 42 1682 x 2 3364 06 3364 842 25 16845 x 5 84225 4852 Find the square root of 70980625 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 84225 without going over 5 is the next digit Subtract 84225 from the last remainder to give zero, terminating the algorithm 0

6. © T Madas

7. 7038409 4 4 6 x 6x 6 303 276 2 Find the square root of 7038409 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

8. © T Madas 7038409 4 4 6 x 6x 6 303 276 2 Find the square root of 7038409 6 276 27 525 x 5x 5 2625 84 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

9. © T Madas 7038409 4 4 6 x 6x 6 303 276 2 Find the square root of 7038409 6 276 27 525 x 5x 5 2625 84 5 2625 159 09 530 3 x 3x 3 15909 3 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 15909 without going over 3 is the next digit Subtract 15909 from the last remainder to give zero, terminating the algorithm 0

10. © T Madas