To determine which among [tex]\(\sqrt[3]{6}\)[/tex], [tex]\(\sqrt{5}\)[/tex], and [tex]\(\sqrt[6]{12}\)[/tex] is the largest, we need to compare the numerical values of these expressions.
1. Calculating [tex]\(\sqrt[3]{6}\)[/tex]:
[tex]\[
\sqrt[3]{6} \approx 1.8171205928321397
\][/tex]
2. Calculating [tex]\(\sqrt{5}\)[/tex]:
[tex]\[
\sqrt{5} \approx 2.23606797749979
\][/tex]
3. Calculating [tex]\(\sqrt[6]{12}\)[/tex]:
[tex]\[
\sqrt[6]{12} \approx 1.5130857494229015
\][/tex]
Now we compare the obtained values:
- [tex]\(\sqrt[3]{6} \approx 1.8171205928321397\)[/tex]
- [tex]\(\sqrt{5} \approx 2.23606797749979\)[/tex]
- [tex]\(\sqrt[6]{12} \approx 1.5130857494229015\)[/tex]
Among the three values, the largest is [tex]\(2.23606797749979\)[/tex], which is the value of [tex]\(\sqrt{5}\)[/tex].
Therefore, the largest among the expressions [tex]\(\sqrt[3]{6}\)[/tex], [tex]\(\sqrt{5}\)[/tex], and [tex]\(\sqrt[6]{12}\)[/tex] is [tex]\(\sqrt{5}\)[/tex].
