Question

Find the cube root of 81: 81−−√3.(1 point)
Responses

−9
negative 9

9
9

81−−√3
root index 3 start root 81 end root

Answer 1

The cube root of 81 can be expressed mathematically as \( \sqrt[3]{81} \).

To find this value, we can calculate:

\[
81 = 3^4
\]

Now, taking the cube root:

\[
\sqrt[3]{81} = \sqrt[3]{3^4} = 3^{4/3} = 3^{1 + 1/3} = 3 \cdot 3^{1/3}
\]

Thus, \( \sqrt[3]{81} \) can be simplified to \( 3 \cdot \sqrt[3]{3} \).

Since we are looking for a numeric approximation, using a calculator gives us:

\[
\sqrt[3]{81} \approx 4.326
\]

So the options given:

- −9
- 9
- \( \sqrt[3]{81} \)

The best response is:

\[
\sqrt[3]{81}
\]

as it represents the cube root of 81 accurately.