Question

5+2 radical3 si 5+3 radical 2
$5 + 2 \sqrt{3}$
$5 + 3 \sqrt{2}$
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Answer 1

$5 + 2 \sqrt{3} = 5 + \sqrt{2 {}^{2} \times 3 } = \\ = 5 + \sqrt{4 \times 3} = 5 + \sqrt{12}$

$5 + 3 \sqrt{2} = 5 + \sqrt{ {3}^{2} \times 2} = \\ = 5 + \sqrt{9 \times 2} = 5 + \sqrt{18}$

$\sqrt{12} < \sqrt{18}$

deci,

$5 + \sqrt{12} < 5 + \sqrt{18} \\ 5 + 2 \sqrt{3} < 5 + 3 \sqrt{2}$