Cube root of 1728 by prime factorisation method

CUBE ROOT OF 1728

The cube root of 1728 is 12. When 12 is multiplied three times by itself, the product we get is 1728.

 How to find the cube root?

To find the cube root of a number easily, we can use the prime factorisation method. On evaluating the prime factors we’ll make the groups of threes of the same digits. Let us take an example of finding the root of 8. By factorisation of 8, we get 8 = 2 x 2 x 2, which is 2³. Now, if we take the cube root on both sides, then the cube of 2 cancels the cube root. Hence, we get the value of ∛8. Therefore, ∛8 = 2

How to calculate the cube root of 1728?

We will use the prime factorization method to get the cube root of 1728.

On performing the prime factorization of 1728

We get, 1728 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3

We can also write it as – 2³ × 2³ × 3³ = (2 × 2 × 3)³

Thus, the cube root of 1728 by prime factorization is ∛(2 × 2 × 3)³ = 12.

Is the cube root of 1728 a rational number, whole number and integer?

Cube root of 1728 is rational because ∛1728 = ∛(2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3) can be expressed as i.e. 12/1 and q is not equal to 0. Therefore, the cube root of 1728 is a rational number.

We know that the whole number includes all natural numbers as well as 0 and the integer includes all whole numbers as well as their negative counterparts. So, 12 is a whole number and an integer.

Hence,  ∛1728 = 12 is a rational number, whole number and an integer.