[tex]3 \sqrt{2} > 2 \sqrt{3} \\ \sqrt{3 {}^{2} \times 2 } > \sqrt{ {2}^{2} \times 3} \\ \sqrt{9 \times 2} > \sqrt{4 \times 3} \\ \sqrt{18} > \sqrt{12} [/tex]
[tex]6 \sqrt{ \frac{2}{3} } =4 \sqrt{ \frac{3}{2} } \\ \sqrt{ \frac{6 {}^{2} \times 2}{3} } = \sqrt{ \frac{ {4}^{2} \times 3}{2} } \\ \sqrt{\frac{36 \times 2}{3} } = \sqrt{ \frac{16 \times 3}{2} } \\ \sqrt{12 \times 2} = \sqrt{8 \times 3} \\ \sqrt{24} = \sqrt{24} [/tex]
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[tex]3 \sqrt{2} > 2 \sqrt{3} \\ \sqrt{3 {}^{2} \times 2 } > \sqrt{ {2}^{2} \times 3} \\ \sqrt{9 \times 2} > \sqrt{4 \times 3} \\ \sqrt{18} > \sqrt{12} [/tex]
[tex]6 \sqrt{ \frac{2}{3} } =4 \sqrt{ \frac{3}{2} } \\ \sqrt{ \frac{6 {}^{2} \times 2}{3} } = \sqrt{ \frac{ {4}^{2} \times 3}{2} } \\ \sqrt{\frac{36 \times 2}{3} } = \sqrt{ \frac{16 \times 3}{2} } \\ \sqrt{12 \times 2} = \sqrt{8 \times 3} \\ \sqrt{24} = \sqrt{24} [/tex]