Is 9270 a perfect cube if not find the smallest number by which it should be divided to get a perfect cube
Answers
Answer:
Step-by-step explanation:
Let's factorize 9720 by LCM.
5 | 9720
2 | 1944
2 | 972
2 | 486
3 | 243
3 | 81
3 | 27
3 | 9
3 | 3
| 1
9720 = 5 x 2^3 x 3^5
∴ 9720 is not a perfect cube.
5 x 2^3 x 3^5 = 9720 divided by 5 x 3^2 = 45 gives a perfect cube. (9720 ÷ 45 = 216 = 2^3 x 3^3 = 6^3)
∴ 45 is the smallest number by which 9720 should be divided to get a perfect prime number
Answer:Let's factorize 9720 by LCM.
5 | 9720
2 | 1944
2 | 972
2 | 486
3 | 243
3 | 81
3 | 27
3 | 9
3 | 3
| 1
9720 = 5 x 2^3 x 3^5
∴ 9720 is not a perfect cube.
5 x 2^3 x 3^5 = 9720 divided by 5 x 3^2 = 45 gives a perfect cube. (9720 ÷ 45 = 216 = 2^3 x 3^3 = 6^3)
∴ 45 is the smallest number by which 9720 should be divided to get a perfect cube.
If the question was meant to find the whole number by which it should be divided to get a perfect cube, the answer will be 45.
But if the question was meant to find the smallest 'fraction', then the answer will be 5/3.
9720 divided by 5/3 gives 18^3.
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