Using the method of successive subtraction, examine whether or not the following numbers are perfect cubes:
(i) 130
(ii) 345
(iii) 792
(iv) 1331.

To do:

We have to find the cube roots of the given numbers by successive subtraction and examine whether or not the given numbers are perfect cubes.

Solution:

(i) $130 - 1 = 129$

$129 -7 = 122$

$122 -19 = 103$

$103 -37 = 66$

$66 - 61 = 5$

Here, 5 is left.

Therefore,

130 is not a perfect cube.

(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,

345 is not a perfect cube.

(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,

792 is not a perfect cube.

(iv) $1331 - 1 = 1330$

$1330 -7 = 1323$

$1323 - 19 = 1304$

$1304 - 37 = 1267$

$1267 - 61 = 1206$

$1206 - 91 = 1115$

$1115 - 127 = 988$

$988 - 169 = 819$

$819 - 217 = 602$

$602 - 271 = 331$

$331 - 331 =0$

Therefore,

1331 is a perfect cube. 

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Updated on: 10-Oct-2022

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