Find the smallest number that must be subtracted from those of the numbers in question 2, which are not perfect cubes, to make them perfect cubes. What are the corresponding cube roots ?

To do:

We have to find the smallest number that must be subtracted from those of the numbers in question 2 which are not perfect cubes, to make them perfect cubes and the corresponding cube roots.

Solution:

From question 2, we find 130, 345 and 792 are not perfect cubes. Therefore,

(i) $130 - 1 = 129$

$129 -7 = 122$

$122 -19 = 103$

$103 -37 = 66$

$66 - 61 = 5$

Here, 5 is left.

Therefore,

5 has to be subtracted from 130 to get a perfect cube.

$130-5=125$

Cube root of 125 is 5.

(ii) $345 - 1 = 344$

$344 - 7 = 337$

$337 - 19 = 318$

$318 - 37 = 281$

$81 - 61 =220$

$220- 91 = 129$

$129 - 127 = 2$

Here, 2 is left.

Therefore,

2 has to be subtracted from 345 to get a perfect cube.

$345-2=343$

Cube root of 343 is 7.

(iii) $792 - 1 = 791$

$791 - 7 = 784$

$784 - 19 = 765$

$765 - 37 = 728$

$728 - 61 = 667$

$667 - 91 = 576$

$576 - 127 = 449$

$449 - 169 = 280$

$280-217=63$

Here, 63 is left.

Therefore,

63 has to be subtracted from 792 to get a perfect cube.

$792-63=729$

Cube root of 729 is 9.