Q. Which of the following are perfect cubes?

1. 400

2. 3375

3. 8000

4. 15625

5. 9000

6. 6859

7. 2025

8. 10648

Answers (2)

We will find it by prime factorization whether they make a pair of three prime numbers or not.

(1)  400 = 2\times2\times2\times2\times5\times5 .   So not a perfect cube.

(2)  3375 = 3\times3\times3\times5\times5\times5.  So it is a perfect cube.

(3)  8000 = 2\times2\times2\times2\times2\times2\times5\times5\times5.  So it is a perfect cube.

(4)  15625 = 5\times5\times5\times5\times5\times5.    So it is a perfect cube.

(5)  9000 = 2\times2\times2\times3\times3\times5\times5\times5.  So it is not a perfect cube.

(6)  6859 = 19\times19\times19.   So it is a perfect cube.

(7)  2025 = 3\times3\times3\times3\times5\times5.   So it is not a perfect cube.

(8)  10648 = 2\times2\times2\times11\times11\times11.  So it is a perfect cube.

We will find it by prime factorisation whether they make pair of three prime numbers or not.

(1)  400 = 2\times2\times2\times2\times5\times5 .   So not a perfect cube.

(2)  3375 = 3\times3\times3\times5\times5\times5.  So it is a perfect cube.

(3)  8000 = 2\times2\times2\times2\times2\times2\times5\times5\times5.  So it is a perfect cube.

(4)  15625 = 5\times5\times5\times5\times5\times5.    So it is a perfect cube.

(5)  9000 = 2\times2\times2\times3\times3\times5\times5\times5.  So it is not a perfect cube.

(6)  9000 = 19\times19\times19.   So it is a perfect cube.

(7)  2025 = 3\times3\times3\times3\times5\times5.   So it is not a perfect cube.

(8)  10648 = 2\times2\times2\times11\times11\times11.  So it is a perfect cube.

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