Question

find the smallest number by which 8640 must be divided so that the quotient is a perfect cube ​

Answer 1

Answer:

it can be divided by numbet 1

Answer 2

Answer:

The required smallest number which 8640 must be divided so that the quotient is a perfect cube is 5.

The required cube root of 1728 is 12

Step-by-step explanation:

To find : The smallest number by which 8640 must be divided so that the quotient is a perfect cube. also find the cube root of the number so obtained.

Solution :

First we factor the number 8640,

8640 = 2*2*2*2*2*2*3*3*3*5

Making a pair of 3,

2^3 * 2^3 * 3^3 * 5

As 5 left alone which means if we divide 8640 by 5 we the the number having a perfect cube.

So, The required smallest number which 8640 must be divided so that the quotient is a perfect cube is 5.

Now, Divide by 8640 by 5

8640/5 = 1728

1728 = (2*2*3)^3

1728 = 12^3

Therefore, The required cube root of 1728 is 12.

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