Question
99= c^3, express your answer kn simplest radical form if necessary
Answers
GPT-4o mini
To solve the equation \(99 = c^3\) for \(c\), we can isolate \(c\) by taking the cube root of both sides.
\[
c = \sqrt[3]{99}
\]
To express \(\sqrt[3]{99}\) in its simplest radical form, we can factor \(99\) into its prime factors:
\[
99 = 3^2 \times 11
\]
Therefore, we can express the cube root as:
\[
c = \sqrt[3]{3^2 \times 11} = \sqrt[3]{3^2} \times \sqrt[3]{11}
\]
Since \(\sqrt[3]{3^2}\) cannot be simplified further since it's not a perfect cube, we can write:
\[
c = \sqrt[3]{9} \times \sqrt[3]{11}
\]
Thus, the simplest radical form of \(c\) is:
\[
c = \sqrt[3]{99}
\]
This is the final answer.
\[
c = \sqrt[3]{99}
\]
To express \(\sqrt[3]{99}\) in its simplest radical form, we can factor \(99\) into its prime factors:
\[
99 = 3^2 \times 11
\]
Therefore, we can express the cube root as:
\[
c = \sqrt[3]{3^2 \times 11} = \sqrt[3]{3^2} \times \sqrt[3]{11}
\]
Since \(\sqrt[3]{3^2}\) cannot be simplified further since it's not a perfect cube, we can write:
\[
c = \sqrt[3]{9} \times \sqrt[3]{11}
\]
Thus, the simplest radical form of \(c\) is:
\[
c = \sqrt[3]{99}
\]
This is the final answer.