Question

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

(i) 3375

(ii) 10648

Answer 1

(i) Resolving 3375 into Prime factors as follows :

Step I. Make groups of three digits, starting from unit place digit as 3 375. 

Step II. 1st group is 375 Its unit place digit is 5 which is obtained only by the cube of any number having unit place digit 5 (5³ = 125) 

So we get 5 at the unit’s place of the cube root.

Step III. IInd group is 3 Which is 1³ < 3 < 2³

Therefore, tens place digit is 1 

∴ ³√3375 = 15

(ii) Resolving 10648 into Prime factors as follows :

Step I. Make groups of three digits, starting from unit place digit as 10648 

Step II. 1st group is 648 Its unit place digit is 8 which can be obtained only by the cube of number having unit place digit as 2 (2³ = 8)

Therefore, we get 2 at the unit place digit of the cube root. 

Step III. Second group is 10 

2³ < 10 < 3³ 

∴ Tens place digit is 2 

Therefore, ³√10648 = 22