Question

FIND tHE SMALLEST NUMBER BY wHICH 192 MUST BE DIVIDED TO OBTAIn A PERFECT CUBE

Answer 1

           

Prime factorization of 192

   

192 = 2⁶ × 3

192 = (2²)³ × 3

When  192 = (2²)³ × 3  is divided by 3, we get (2²)³ = 4³ = 64.

∴ 3 is the answer.

Plz mark it as the brainliest.

Thank you. :-))

           

Answer 2

Answer: The smallest number is 3.

Step-by-step explanation:

Given that:

A number 192 is given.

We have to find the smallest number by which it is divided to obtain a perfect cube.

Finding the smallest number:

• prime factorization of 192:

$192=2^{6}*3$

• making it perfect cube:

$192=(2^{2} )^{3}*3$

here we get perfect cube of square of 2 equal to 4 that is $4*4*4=64$ and an extra 3 in factor of 192.

In order to make 192 perfect cube of 4 that is 64. Then we have to eliminate 3 from the factor of 192.

therefore, we divide 192 by 3 to make it a perfect square which is also the smallest number.

Hence, the smallest number here is 3.