Question

Is 9720 a perfect cube ? If not, find the smallest number by which it should be divided to get a perfect cube.

Answer 1

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.

Hope this may be helpful.

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Answer 2

Answer:

factorize 9720 byLCM

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

so 9720 is not a perfect cube.

now to check smallest no. to be divided to make a perfect cube.. 5 x 3^2 = 45 gives a perfect cube. (9720 ÷ 45 = 216 = 2^3 x 3^3 = 6^3)

so 45 is the smallest no. to be divided by 9720 to make a perfect cube

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