Question

Check whether 1728 is a perfect cube by using prime factorisation.
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Answer 1

Answer:

Cube & Cube Roots: Theory and Solved Examples

Now in order to find the cube root of a number the only method available is prime factorization. ...

Prime factorization of 1728 is = 2 * 2 * 2 * 2 * 2 * 2 * 3 * 3 * 3. ...

= (7 * 3) * (7 * 3) * (7 × 3) ...

= (5 * 5) * (5 * 5) * (5 * 5)

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Answer 2

Answer:

Step-by-step explanation:

prime factorization

1728= 2-1728

          2-864

          2-432

          2-216

          2-108

           2-54

         3-27

         3-9

       3 -3

            1

1728=2*2*2*2*2*2*3*3*3

   $3^{3}$ *$2^{3}$*$2^{3}$

3*2*2=12

hence 1728 is a perfect cube.