[tex]4 \sqrt{12} = 4 \sqrt{2 {}^{2} \times 3} = 4 \times 2 \sqrt{3} = \\ = 8 \sqrt{3} [/tex]
[tex]3 \sqrt{8} = 3 \sqrt{2 \times 2 \times 2} = 3 \sqrt{ {2}^{2} \times 2} = \\ 3 \times 2 \sqrt{2} = 6 \sqrt{2} [/tex]
[tex]3 \sqrt{40} = 3 \sqrt{4 \times 10} = \\ = 3 \sqrt{2 {}^{2} \times 2 \times 5} = 3 \times 2 \sqrt{10} \\ = 6 \sqrt{10} [/tex]
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[tex]4 \sqrt{12} + 3 \sqrt{8} + 3 \sqrt{40} = \\ =8 \sqrt{3} + 6\sqrt{2} + 6 \sqrt{10} [/tex]
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[tex]2 \sqrt{18} = 2 \sqrt{9\times2 } = 2 \sqrt{3 {}^{2} \times 2 } = \\ = 2 \times 3 \sqrt{2} = 6 \sqrt{2} [/tex]
[tex]2 \sqrt{48} = 2 \sqrt{ {2}^{4} \times 3} = 2 \times 2 {}^{2} \sqrt{3} = \\ = {2}^{3} \sqrt{3} = 8 \sqrt{3} [/tex]
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[tex]2 \sqrt{18} + 2 \sqrt{48} + 19 = \\ = 6 \sqrt{2 } + 8 \sqrt{3} + 19[/tex]
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Comparăm:
8✓3+6✓2+6✓10 și 6✓2+8✓3+19
observăm că ambele nunere au 8✓3+6✓2
deci comparam termenii diferiți
6✓10 și 19
[tex]6 \sqrt{10} = \sqrt{ {6}^{ 2} \times 10 } = \sqrt{36 \times 10} = \\ = \sqrt{360} \\ 19 = \sqrt{19 {}^{2} } = \sqrt{361} [/tex]
361 > 360
19 > 6✓10
6✓2+8✓3+19 > 8✓3+6✓2+6✓10
4✓12+3✓8+3✓40 > 2✓18+2✓48+19
