Question

42. Find the cube root of the following by the method of successive subtraction of the numbers 1, 7, 19, 37, 61, 91, 127, 169, 217, 271, 331, 397,... (a) 125 .(b) 343 (c) 2197​

Answer 1

Answer:

a)5 b) 7 c) 13

Step-by-step explanation:

125-1=124, 124-7=117, 116-19= 98, 98-37=61, 61-61=0

That is, we obtain the difference is 0 after 5 successive subtractions.

∴ The cube root of 125=5.

343-1=342, 342-7=335, 335-19= 316, 316-37=279, 279-61=218, 218-91=127, 127-127= 0

That is, we obtain the difference is 0 after 7 successive subtractions.

∴ The cube root of 343=7.

2197-1=2196, 2196-7=2187, 2187-19= 2170, 2170-37=2133, 2133-61=2072, 2072-91=1981, 1981-127=1857, 1857-169=1685,1685-217=1468,1468-271=1197,1197-331=886,886-397=469,

469-469 =0

That is, we obtain the difference is 0 after 13 successive subtractions.

∴ The cube root of 2197=13.