Question

what is the smallest number by which 784 be multiplied so that the product become perfect cube? Also show the process

Answer 1

Hello Dear!!!

Here's your answer...

The given number is

784

First,we have to do prime factorisation

784 - 2^4 * 7^2

Here,

The power of 2 is 4...
To become a perfect cube..then the power should be a multiple of 3

Then, it should be multiplied with two 2's to become power 6(multiple of 3)

And power of 7 is 2
It should be multiplied with one 7....to become power 3(power should be multiple of 3)

Then,

It should be multiplied with 2*2*7

28

Finally...it should be multiplied with 28 to get perfect cube

Verification -

784 * 28

21952

It is cube root of 28

______________________

Hope this helps you.....

Answer 2

Answer:

784=2×2×2×2×7×7

784×2×2×7=2×2×2×2×2×2×7×7×7

784×28=21952

if we multiply 28 with 784, it becomes a perfect cube.