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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To rewrite the irrational cube root 189√3 as the product of an integer and another irrational cube root, we can simplify the cube root of 189.
Let's write 189 as 27 * 7. Therefore, we can express the cube root of 189 as:
∛189 = ∛(27 * 7) = ∛27 * ∛7 = 3√7
So we have ∛189 = 3√7
Therefore, the irrational cube root ∛189 can be expressed as the product: 3 * √7