Question

find the smallest number by which 192 must be divided to obtain a perfect cube ​

Answer 1

Answer:

3 is the answer

Step-by-step explanation:

By prime factorisation method, we have

192= 2×2×2×2×2×2×3

=(2³×2³×3)

=((2×2)³×3)

In the above factorization there is no triplet for 3.

So, 192 is not a perfect cube.

Therefore, 192 must be divided by 3 to make the quotient a perfect cube.

Answer 2

Here, we have to find the smallest  by which 192 must be divided to obtain a perfect cube .

For that , firstly we must perform the prime factorization of 192.

192 = 2 × 2 × 2 × 2 × 2 × 2 × 3

During the process of finding cube root we must group three numbers as one, i.e

192 = 2 × 2 × 2  × 2 × 2 × 2  × 3

∴ 192 = 2 × 2 × 3

Here the only number which cannot be grouped is 3 .

So 192 must be divided by 3 to obtain a perfect cube ​.

To Verify

192 ÷ 3 = 64

We , know that 64 is the cube of 4.

Hence, our Answer is correct