Rewrite the irrational cube root root(189, 3) as the product of an integer and another irrational cube root. Show your work.

Question

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(2 points)

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Answer 1

To rewrite the irrational cube root ∛189 as the product of an integer and another irrational cube root, we can split the prime factorization of 189 into perfect cube factors.

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

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

Taking the cube root of 3 * 3, we get ∛(3 * 3) = 3.

The remaining factor is 3 * 7, which is 21. So, the cube root of 21 is ∛21.

Therefore, ∛189 can be rewritten as 3 * ∛21.