Question

Find 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 277–√3 27 root index 3 start root 7 end root 37–√

Answer 1

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

189 can be factored as:
\[
189 = 3^3 \times 7
\]

Now, we will take the cubic root:
\[
\sqrt[3]{189} = \sqrt[3]{3^3 \times 7}
\]

Using the property of cube roots:
\[
\sqrt[3]{a \times b} = \sqrt[3]{a} \times \sqrt[3]{b}
\]
we get:
\[
\sqrt[3]{189} = \sqrt[3]{3^3} \times \sqrt[3]{7} = 3 \times \sqrt[3]{7}
\]

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

From your provided options, the correct one is:
\[
3 \text{ root index } 3 \text{ start root } 7 \text{ end root}
\]

Thus, the answer is:
\[
3 \sqrt[3]{7}
\]