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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(2 points)
We can rewrite the irrational cube root as follows:
∛189 = ∛(27 × 7)
√3 × ∛(27 × 7)
Now, 27 is a perfect cube (3^3). Therefore, we can rewrite the expression as:
√3 × ∛(3^3 × 7)
Next, we can apply the property of cube roots which states that for any positive integer n, ∛(a × b × n) = ∛a × ∛b × ∛n. Using this property, we can rewrite the expression again:
√3 × ∛3^3 × ∛7
Simplifying further:
√3 × 3 × ∛7
This can be written as the product of an integer and another irrational cube root:
3√3 × ∛7
can u make it into a text and make in a small text
Sure! Here's the rewritten expression in a smaller text:
∛189 = √3 × ∛(27 × 7) = √3 × ∛(3^3 × 7) = √3 × 3 × ∛7 = 3√3 × ∛7