Question

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

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

37–√3
3 root index 3 start root 7 end root

37–√
3 start root 7 end root

277–

Answer 1

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

First, we can simplify \( \sqrt[3]{189} \):
189 can be factored into \( 3^3 \times 7 \), since \( 189 = 27 \times 7 = 3^3 \times 7 \).

Now using the property of cubic roots:
\[
\sqrt[3]{189} = \sqrt[3]{3^3 \times 7} = \sqrt[3]{3^3} \times \sqrt[3]{7} = 3 \times \sqrt[3]{7}
\]

Therefore, the cubic root of 189 is:
\[
3 \sqrt[3]{7}
\]

From your options, the correct response corresponding to this value is:
\[
3 \text{ root index } 3 \text{ start root } 7 \text{ end root}
\]