Question

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

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

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

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

37–√

Answer 1

To find the cubic root of 189, we can start by simplifying it as much as possible.

First, we can factor 189:
\[ 189 = 3^3 \times 7 \]

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

Using the property of cubic roots:
\[ \sqrt[3]{a \times b} = \sqrt[3]{a} \times \sqrt[3]{b} \]

This gives us:
\[ \sqrt[3]{189} = \sqrt[3]{3^3} \times \sqrt[3]{7} = 3 \times \sqrt[3]{7} \]

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

Looking at your options, this corresponds to:
- **37–√3** (which seems to represent \(3 \sqrt[3]{7}\))

So the answer is \( 3 \sqrt[3]{7} \).