. Rewrite the irrational cube root ^3√189 as the product of an integer and another irrational cube root. Show your work.

1 answer

To rewrite the irrational cube root as the product of an integer and another irrational cube root, we need to find a perfect cube that is a factor of 189.

We can find that the perfect cube 27 is a factor of 189. Therefore, we can rewrite ∛189 as ∛(27 * 7).

Breaking it down further, we have ∛(27 * 7) = ∛27 * ∛7.

The cube root of 27 (∛27) is 3, which gives us 3 * ∛7.

Therefore, the irrational cube root ∛189 can be rewritten as the product of an integer (3) and another irrational cube root (∛7).