Using the method of successive subtraction examine whether or not the following numbers are perfect cubes:
Question:
Using the method of successive subtraction examine whether or not the following numbers are perfect cubes:
(i) 130
(ii) 345
(iii) 792
(iv) 1331
Solution:
(i)
We have:
$\because$ The next number to be subtracted is 91 , which is greater than 5 .
$\therefore 130$ is not a perfect cube.
(ii)
We have:
$\because$ The next number to be subtracted is 161 , which is greater than 2 .
$\therefore 345$ is not a perfect cube.
(iii)
We have:
$\because$ The next number to be subtracted is 271 , which is greater than 63 .
$\therefore 792$ is not a perfect cube.
(iv)
We have:
$\because$ The subtraction is performed 11 times.
$\therefore \sqrt[3]{1331}=11$
Thus, 1331 is a perfect cube.