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

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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 .

Updated on 10-Oct-2022 12:46:49