Question

2√3 и 3√2 ;
2√5 и 3√2 ;
√23 и 2√6 ;
2/3√72 и 13√2/3.
ответы сравнить и желательно поэтапно ПЛИИИЗ​

Answer 1

1.

$2 \sqrt{3} = \sqrt{4} \sqrt{3} = \sqrt{4 \times 3} = \sqrt{12} \\ 3 \sqrt{2} = \sqrt{9} \sqrt{2} = \sqrt{18} \\ \sqrt{18} > \sqrt{12} \\ 3 \sqrt{2} > 2 \sqrt{3}$

2.

$3 \sqrt{2} = \sqrt{18} \\ 2 \sqrt{5} = \sqrt{4} \sqrt{5} = \sqrt{20} \\ \sqrt{20} > \sqrt{18} \\ 2 \sqrt{5} > 3 \sqrt{2}$

3.

$2 \sqrt{6} = \sqrt{4} \sqrt{6} = \sqrt{24} \\ \sqrt{24} > \sqrt{23} \\ 2 \sqrt{6} > \sqrt{23}$

4.

$\frac{2}{3} \sqrt{72} = \sqrt{ \frac{ {2}^{2} }{ {3}^{2} } } \sqrt{72} = \sqrt{ \frac{4}{9} } \sqrt{72} = \sqrt{ \frac{4 \times 72}{9} } = \sqrt{4 \times 8} = \sqrt{32} \\ \\ 13 \sqrt{ \frac{2}{3} } = \sqrt{169} \sqrt{ \frac{2}{3} } = \sqrt{ \frac{169 \times 2}{3} } = \sqrt{ \frac{338}{3} } = \sqrt{112 \frac{2}{3} } \\ \sqrt{112 \frac{2}{3} } > \sqrt{32} \\ 13 \sqrt{ \frac{2}{3} } > \frac{2}{3} \sqrt{72}$