Square Roots with Newton's Method

square root of

2

number of iterations

6

number of decimal places

5

10

20

50

2.0000000000000000000000000000000000000000000000000

1.5000000000000000000000000000000000000000000000000

1.4166666666666666666666666666666666666666666666667

1.4142156862745098039215686274509803921568627450980

1.4142135623746899106262955788901349101165596221157

1.4142135623730950488016896235025302436149819257762

1.4142135623730950488016887242096980785696718753772

Estimate square roots using Newton's method to varying accuracy by controlling the number of iterations and the precision of the estimates. Successively better estimations are shown.