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

Answer 1

To simplify the cube root of 189, we can break down 189 into its prime factorization:

189 = 3 × 3 × 3 × 7

Since the cube root of 189 involves √3, we can rewrite it as:

∛189 = ∛(3 × 3 × 3 × 7) = ∛(3^3 × 7)

We can take out the cube root of 3^3 since it is a perfect cube, and it simplifies to 3:

∛189 = 3 × ∛7

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