Question

Find the cubic root of 189.(1 point) Responses 37–√3 3 root index 3 start root 7 end root 277–√3 27 root index 3 start root 7 end root 921−−√3 9 root index 3 start root 21 end root 37–√

Answer 1

To find the cubic root of 189, we denote it as \( \sqrt[3]{189} \).

To simplify \( \sqrt[3]{189} \), we should factor 189:

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

Now, taking the cubic root:

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

Thus, the cubic root of 189 is:

\[
3 \sqrt[3]{7}
\]

Among the options provided, it seems that the closest matching response is:

**3 root index 3 start root 7 end root**, which represents \( 3\sqrt[3]{7} \).