Question
Rewrite the irrational cube root 189−−−√3 as the product of an integer and another irrational cube root. Show your work.
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GPT 3.5
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).
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).
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