⁶√5 < √2 < ³√3
Step-by-step explanation:
Given: ⁶√5, ³√3, √2
[tex] = {5}^{ \frac{1}{6} } , \: {3}^{ \frac{1}{3} } , \: {2}^{ \frac{1}{2} } \\ = {({5}^{ \frac{1}{6} })}^{6} , \: {({3}^{ \frac{1}{3} })}^{6} , \: {({2}^{ \frac{1}{2} })}^{6} \\ = 5, \: {3}^{2} , \: {2}^{3} \\ = 5, \: 9, \: 8 \\ \\ 5 < 8 < 9 \\ = {5}^{ \frac{1}{6} } < \: {2}^{ \frac{1}{2} } \: < {3}^{ \frac{1}{3} } \\ [/tex]
