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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
To do:
We have to find the cube roots of the given numbers by successive subtraction of numbers: 1, 7, 19, 37, 61, 91, 127, 169, 217, 271, 331, 397.
Solution:
(i) $64 - 1 = 63$
$63 - 7 = 56$
$56 - 19 = 37$
$37 - 37 = 0$
This implies,
$64 = (4)^3$
Therefore,
Cube root of 64 is 4 .
(ii) $512 -1 =511$
$511- 7 = 504$
$504 - 19 = 485$
$485 - 37 = 448$
$448 - 61 = 387$
$387 - 91 =296$
$296 - 127 = 169$
$169 - 169 = 0$
This implies,
$512 = (8)^3$
Therefore,
Cube root of 512 is 8 .
(iii) $1728 - 1= 1727$
$1727 -7 = 1720$
$1720 -19 = 1701$
$1701 -37= 1664$
$1664 - 61 = 1603$
$1603 - 91 = 1512$
$1512 -127= 1385$
$1385 - 169= 1216$
$1216 - 217 = 999$
$999 - 271 =728$
$728 - 331 = 397$
$397 - 397=0$
This implies,
$1728 = (12)^3$
Therefore,
Cube root of 1728 is 12 .
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