Question

find the number by which 55296 we divided so that the quotient is a perfect cube also find the cube root of the quotient​

Answer 1

Answer:

Step-by-step explanation:

Given number = 55296.

Let us first find the Prime Factors of 55296.

We have-   2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3

Thus, Making the Groups of three similar numbers,

  ∴    2 × 2 × 2      2 × 2 × 2      2 × 2 × 2        2 × 2          3 × 3 × 3

         ↔↔↔          ↔↔↔         ↔↔↔                            ↔↔↔↔

Since the Prime Factor 2 does not appear in the group of 3.

∴ If we divide the 55296 by 2 × 2 = 4, then the left out 2's will be not there.

So the smallest number by which 55296 should be divided is 4 and the number thus obtained is 55296/4 = 13824, which is a perfect cube.

Thus, the Required Answer is 13824.

Cube root of the Above Answer is 24.