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

Question

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Answer 1

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

Let's break down 189 into its prime factorization:
189 = 3 × 3 × 3 × 7

Since we are looking for a perfect cube, we can take out three 3's from 189, leaving us with 7.

Now we can rewrite 3^√189 as 3^√(3 × 3 × 3) × 3^√7.

Simplifying, we get: 3^3 × 3^√7.

So, the rewritten form is 27 × 3^√7.