Question

p = 6048. p*r is a cube number, where r is an integer. Find the smallest possible value of r​

Answer 1

Step-by-step explanation:

P=32×27×7

To make it a perfect cube we have to multiply it at least by 2×49=98=R.

Answer 2

98 is the smallest possible value of r. The number is 84 cube.

Step-by-step explanation:

The given p-value is

$p=6048$

The given is $\[p\times r\]$ is a cube number.

$\[p\times r=r\times 6048\]$

$\[=r\times 8\times 27\times 2\times 2\times 7\]$

To make $\[p\times r\]$ a cube number,

r needs to be replaced by $2\times 7\times 7$ that is 98.

Now $\[p\times r\]$ becomes $8\times 27\times 2\times 2\times 7\times 2\times 7\times 7$ which is a cube of 84.

To make it a perfect cube we have to multiply it at least by $2\times 49=98$

Therefore the smallest possible value of r is 98.