Question:
Find the cube roots of the following numbers by successive subtraction of numbers:
1, 7, 19, 37, 61, 91, 127, 169, 217, 271, 331, 397, ...
(i) 64
(ii) 512
(iii) 1728
Solution:
(i)
We have:
$\because$ Subtraction is performed 4 times.
$\therefore \sqrt[3]{64}=4$
(ii)
We have:
$\because$ Subtraction is performed 8 times.
$\therefore \sqrt[3]{512}=8$
(iii)
We have:
$\because$ Subtraction is performed 12 times.
$\therefore \sqrt[3]{1728}=12$