Question

Find the cube roots of the following numbers by estimate and prime factor method. Verify your answer

(i) 46656

(ii) 91125

Answer 1

(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