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

Responses

9
9

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

−9
negative 9

27

1 answer

To find the cube root of 81, we can express it as:

\[ 81^{1/3} \]

Since \(81\) can be expressed as \(3^4\) (because \(3^4 = 81\)), we can rewrite the cube root as:

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

Thus, the cube root of \(81\) does not simplify to a whole number. The approximate decimal value of \(81^{1/3}\) is about \(4.326\).

None of the provided responses (9, \(81^{1/3}\), -9, 27) are correct since \(81^{1/3}\) is not a whole number.

However, if you're looking for the expression for the cube root of 81, the correct answer would be:

\(81^{1/3}\).