Question

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

(i) 64 

(ii) 343

Answer 1

(i) Resolving 64 into Prime factors as follows :

Step I. Make groups of three digits, starting from unit place digit as 064 

Step II. 1st group is 64. Its unit digit is 4 which is obtained only by the cube of a number whose unit digit is 4 (4³ = 64) 

Therefore, cube root of 64 is 4.

(ii) Resolving 343 into Prime factors as follows :

Step I. Make group of three digits, starting from unit place digit as 343 

Step II. First group is 343. Its unit digit is 3 which is obtained only by the cube of a number whose unit digit is 7 (7³ = 343) 

∴ Cube root of 343 is 7.