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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)

best_answer

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.

Posted by

Devendra Khairwa

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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.

Posted by

Devendra Khairwa

View full answer

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