Find the cubic root of 189.(1 point)

Question

Responses

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

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

37–√
3 start root 7 end root

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

Answer 1

To find the cubic root of \(189\), we can express it in a more manageable form.

We first factor \(189\): \[ 189 = 3 \times 63 = 3 \times 3 \times 21 = 3^3 \times 7 \]

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

So, the cubic root of \(189\) is \(3\sqrt[3]{7}\).

Among the provided options, the correct response is: \[ 3\sqrt[3]{7} \]