Question

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

Answer 1

[AI-generated answer — Bot GPT 3.5]

To rewrite the irrational cube root ^3 189 as the product of an integer and another irrational cube root, we need to find a perfect cube that is a factor of 189.

The prime factorization of 189 is: 3 * 3 * 3 * 7.

We can rewrite 189 as (3 * 3 * 3) * 7.

Taking the cube root gives us:

∛(189) = ∛(3 * 3 * 3) * ∛(7)

Simplifying the cube root of 27:

∛(3 * 3 * 3) = 3

So, we have:

∛(189) = 3 * ∛(7)

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