Extraction of square root

Square root of 18983449: start with the number and a marker above the units digit x 1 8 9 3 4

Move the marker two places to the left. x 1 8 9 3 4

Move the marker two places to the left. x 1 8 9 3 4

Move the marker two places to the left. x 1 8 9 3 4

Replace by marker by the largest integer whose square is no more than the number below it. In this case it is 4. x 1 8 9 3 4

Substract the square of this digit from the number below it. 4 1 8 9 3 6 2

Write the next two digits from the dividend; multiply the quotient by 20 and find the largest possible digit x such that x(20quotient + x) does not exceed this number. In this case, this digit is 3. 4 x 1 8 9 3 6 2

Write the next two digits from the dividend; multiply the quotient by 20 and find the largest possible digit x such that x(20quotient + x) does not exceed this number. In this case, this digit is 3. 4 3 1 8 9 6 2

Write the next two digits from the dividend; multiply the quotient by 20 and find the largest possible digit x such that x(20quotient + x) does not exceed this number. In this case, this digit is 5. 4 3 x 1 8 9 6 2

Write the next two digits from the dividend; multiply the quotient by 20 and find the largest possible digit x such that x(20quotient + x) does not exceed this number. In this case, this digit is 7. 4 3 5 x 1 8 9 6 2 7

Write the next two digits from the dividend; multiply the quotient by 20 and find the largest possible digit x such that x(20quotient + x) does not exceed this number. In this case, this digit is 7. 4 3 5 7 1 8 9 6 2

The square root of 18983449 is 4357 4 3 5 7 1 8 9 6 2