Question

Find the cubic root of 189.(1 point)
Responses

921−−√3
9 root index 3 start root 21 end root

37–√
3 start root 7 end root

277–√3
27 root index 3 start root 7 end root

37–√3

Answer 1

To find the cubic root of 189, we can express 189 in terms of its prime factorization:

189 = 3^3 * 7

Now, we can take the cube root:

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

Thus, the cubic root of 189 can be written as:

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

Among the given options, the one that corresponds to \( 3 \sqrt[3]{7} \) is:

**37−−√3 start root 7 end root**