Question

Qual a raiz cúbica de 100 até a quarta casa decimal, por frações contínuas ou pela suas reduzidas?Passo a passo.

Answer 1

Olá Valpino

³√100 

frações continuas

[4; 1, 1, 1, 3, 1, 3, 4, 4, 1, 1, 3, 1, 16, 1, 1, 1, 5, 8, 5,  ...]

8 + 1/5 = 41/5 

5 + 5/41 = 210/41 

1 + 41/210 = 251/210 

1 + 210/251 = 461/251 

1 + 251/461 = 712/461 

16 + 461/712 = 11853/712

1 + 712/11853 = 12565/11853

3 + 11853/12565 = 49548/12565

1 + 12565/49548 = 62113/49548

1 + 49548/62113 = 111661/62113

4 + 62113/111661 = 508757/111661

4 + 111661/508757 = 2146689/508757

3 + 508757/2146689 = 6948824/2146689

1 + 2146689/6948824 = 9095513/6948824

3 + 6948824/9095513 = 34235363/9095513

1 + 9095513/34235363 = 43330876/34235363

1 + 34235363/43330876 = 77566239/43330876

1 + 43330876/77566239 = 120897115/77566239

4 + 77566239/120897115 = 561154699/120897115 

³√100 = 4.64159