Question

. Is 5625000 a perfect cube? Explain.

Answer 1

Here is your answer

Answer 2

Solution :-

To find whether a number is a perfect cube or not, the most straight forward method is to check through factorization. If the prime factors of a number are grouped in triplets of equal factors, then that number will be called a perfect cube.

We will examine 5625000

______________

2 | 5625000

_______________

2 | 2812500

|______________-

2 | 1406250

|______________

3 | 703125

|______________

3 | 234375

|______________

5 | 78125

|______________

5 | 15625

|______________

5 | 3125

|______________

5 | 625

|______________

5 | 125

|_____________

5 | 25

|____________

5 | 5

|____________

| 1

Prime factors of 5625000 = 2 × 2 × 2 × 3 × 3 × 5 × 5 × 5 × 5 × 5 × 5 × 5

Prime factors 3 and 5*5 are not parts of a triplet. So, 5625000 is not a perfect cube.