Question

Find the smallest number by which 8640 should be divided to make quotient a perfect cube. Also find the cube root of the quotient.​

Answer 1

Step-by-step explanation:

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 \times 2\times2\times2\times2\times2 \times3\times3\times3 \times 58640=2×2×2×2×2×2×3×3×3×5

Making a pair of 3,

8640=2^3\times2^3 \times3^3 \times 58640=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 5

\frac{8640}{5}=\frac{2^3\times2^3 \times3^3 \times 5}{5}

5

8640

=

5

2

3

×2

3

×3

3

×5

1728=(2\times2\times3)^31728=(2×2×3)

3

1728=(12)^31728=(12)

3

Therefore, The required cube root of 1728 is 12.