Question

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

(i) 5832

(ii) 74088

Answer 1

(i) Resolving 5832 into Prime factors as follows :

Step I. Make groups of three digits starting from unit place digits as 5832 

Step II. 1st group is 832 and its unit place digit is 2 which is obtained only by the cube a number whose unit digit is 8 

(8³ = 512) 

So, we get 8 at the unit place digit of the cube root. 

Step III. Second group is 5 which is greater than cube of 1 and smaller than cube of 2 

∴ 1³ < 5 < 2³ 

Therefore, tens place digit is 1 . 

Therefore, Cube root of ³√5832 = 18

(ii) Resolving 74088 into Prime factors as follows :

Step I. Make groups of three digits starting from unit place digit as 77088 

Step II. 1st group is 088, its unit digit 8 which is obtained by the cube of 2 i.e. (2³ = 8) 

∴ We get 2 at the unit places digit of the cube root. 

Step III. IInd group is 74 

Therefore, 4³ < 74 < 5³ 

∴ Ten place digit is 4.

Therefore. ³√74088 = 42