Question

Rewrite the irrational cube root 3√189 as the product of an integer and another irrational cube root. Show your work in the least amount of sentences.

Answer 1

To rewrite \( \sqrt[3]{189} \) as the product of an integer and another cube root, we start by factoring \( 189 \):

\[
189 = 3^3 \times 7
\]

Now we can rewrite the cube root:

\[
\sqrt[3]{189} = \sqrt[3]{3^3 \times 7} = \sqrt[3]{3^3} \times \sqrt[3]{7} = 3 \times \sqrt[3]{7}
\]

Thus, \( \sqrt[3]{189} = 3 \sqrt[3]{7} \).