1. Trial and Improvement
Cube root

2. x3 = 17 x x3

3. x3 = 17 x x3 2

4. x3 = 17 x x3 2
2 x 2 x 2 = 8

5. x3 = 17 x x3 2
2 x 2 x 2 = too small

6. x3 = 17 x x3 2
2 x 2 x 2 = too small 3

7. x3 = 17 x x3 2
2 x 2 x 2 = too small 3
3 x 3 x 3 = 27

8. x3 = 17 x x3 2
2 x 2 x 2 = too small 3
3 x 3 x 3 = too big

9. x3 = 17 x x3 2
2 x 2 x 2 = too small 3
3 x 3 x 3 = too big
2.5

10. x3 = 17 x x3 2 2 x 2 x 2 = 8 too small 3 3 x 3 x 3 = 27 too big 2.5
2.53

11. x3 = 17 x x3 2 2 x 2 x 2 = 8 too small 3 3 x 3 x 3 = 27 too big 2.5
2.53 =

12. x3 = 17 x x3 2 2 x 2 x 2 = 8 too small 3 3 x 3 x 3 = 27 too big 2.5

13. x3 = 17 x x3 2 2 x 2 x 2 = 8 too small 3 3 x 3 x 3 = 27 too big 2.5
2.6

14. x3 = 17 x x3 2 2 x 2 x 2 = 8 too small 3 3 x 3 x 3 = 27 too big 2.5
2.6
2.63

15. x3 = 17 x x3 2 2 x 2 x 2 = 8 too small 3 3 x 3 x 3 = 27 too big 2.5
2.6
2.63 =

16. x3 = 17 x x3 2 2 x 2 x 2 = 8 too small 3 3 x 3 x 3 = 27 too big 2.5
2.6
2.63 = too big

17. x3 = 17 x x3 2 2 x 2 x 2 = 8 too small 3 3 x 3 x 3 = 27 too big 2.5
2.6
2.63 = too big
2.55

18. x3 = 17 x x3 2 2 x 2 x 2 = 8 too small 3 3 x 3 x 3 = 27 too big 2.5
2.6
2.63 = too big
2.55
2.553 =

19. x3 = 17 x x3 2 2 x 2 x 2 = 8 too small 3 3 x 3 x 3 = 27 too big 2.5
2.6
2.63 = too big
2.55
2.553 =
Does the solution lies between 2.5 and 2.55
or between 2.55 and 2.6?
So the solution between 2.55 and 2.6 to 1 d.p. is 2.6