Question

Which of the following numbers is a cube number ? *

(a) 1000
(b) 400
(c) 100
(d) 600
​

Answer 1

(a) 1000

1000 is a cube number.

Explanation:

(a) 1000

Here 1000 = 2 × 2 × 2 × 5 × 5 × 5

Each of 2 and 5 appears three times and thus satisfies the condition for cube numbers.

(b) 400

Here 400 = 2 × 2 × 2 × 2 × 5 × 5

2 appears four times and 5 appears two times and thus 400 is not a cube number.

(c) 100

Here 100 = 2 × 2 × 5 × 5

Each of 2 and 5 appear twice and thus 100 is not a cube number.

(d) 600

Here 600 = 2 × 2 × 2 × 3 × 5 × 5

3 appears once and 2 appears twice and thus 600 is not a cube number.

Hint:

If a number has its prime factors appearing as a multiple of 3, then that number is a cube number.

Answer 2

Answer:

Which of the following numbers is a cube number ? *

(a) 1000

(b) 400

(c) 100

(d) 600

1000 is the answer