[tex]5 + 2 \sqrt{3} = 5 + \sqrt{2 {}^{2} \times 3 } = \\ = 5 + \sqrt{4 \times 3} = 5 + \sqrt{12} [/tex]
[tex]5 + 3 \sqrt{2} = 5 + \sqrt{ {3}^{2} \times 2} = \\ = 5 + \sqrt{9 \times 2} = 5 + \sqrt{18} [/tex]
[tex] \sqrt{12} < \sqrt{18} [/tex]
deci,
[tex]5 + \sqrt{12} < 5 + \sqrt{18} \\ 5 + 2 \sqrt{3} < 5 + 3 \sqrt{2} [/tex]
