(i) Resolving 46656 into Prime factors as follows :
Step I. Make groups of three digits starting from unit place digit as 46 656
Step II. 1st group is 656. Its unit place digit is 6 which is obtained by the cube of any number having unit place digit as 6.
We know that 63 = 216
Step III. Second group is 46
33 < 46 < 43
∴ Ten place digit is 3
Hence, cube root of 46656 is 36
∴³√46656 = 36
(ii) Resolving 91125 into Prime factors as follows :
Step I. Make digit of three digits, starting from unit place digit 91 125
Step II. 1st group is 125. Its unit place digit is 5 which is obtained only by the cube of any number having unit place digit as 5
(53 = 125)
Step II. IInd group is 91
Here 43<91<53
Therefore,tens place digit is 4
Therefore, ³√91125 = 45