Question

The given numbers are cubes of certain numbers. Find these numbers.

(1) 4096
(2) 4913
(3) 5832
(4) −2197

Answer 1

(1) 4096 can be written in terms of its prime factors as:
4096 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
All these factors can be grouped as:
4096 = (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2)
So, the cube root of 4096 = 2 × 2 × 2 × 2 = 16.

(2) 4913 can be written in terms of its prime factors as:
4913 = 17 × 17 × 17
So, 17 is the cube root of 4913.

(3) 5832 can be written in terms of its prime factors as:
5832 = 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 3
All these factors can be grouped as:
5832 = (2 × 2 × 2) × (3 × 3 × 3) × (3 × 3 × 3)
So, the cube root of 5832 = 2 × 3 × 3 = 18.

(4) To find the cube root of −2197 , we shall first find the cube root of 2197.
2197 can be written in terms of its prime factors as:
2197 = 13 × 13 × 13
13 is the cube root of 2197.
So, −13 is the cube root of −2197.