Răspuns:

Explicație pas cu pas:

Verified answer

Explicație pas cu pas:

c)

[tex]3 \sqrt{2} = \sqrt{2 \cdot {3}^{2}} [/tex]

[tex]\sqrt{27} = \sqrt{ {3}^{3} } [/tex]

[tex]2 \cdot {3}^{2} < {3}^{3} \implies \sqrt{2 \cdot {3}^{2}} < \sqrt{27} \\ \iff 3 \sqrt{2} < \sqrt{27} \\ [/tex]

e)

[tex]{3}^{3} \sqrt{18} = \sqrt{ {3}^{6} \cdot 2 \cdot {3}^{2} } = \sqrt{2 \cdot {3}^{8} }[/tex]

[tex]{9}^{3} \sqrt{2} = {( {3}^{2} )}^{3} \sqrt{2} = {3}^{6} \sqrt{2} = \sqrt{2 \cdot {3}^{12}}[/tex]

[tex]{3}^{8} < {3}^{12} \iff 2 \cdot {3}^{8} < 2 \cdot {3}^{12} \implies \\ \sqrt{2 \cdot {3}^{8} } < \sqrt{2 \cdot {3}^{12} } \iff {3}^{3} \sqrt{18} < {9}^{3} \sqrt{2} \\ [/tex]