8. Która z poniższych liczb jest równa 24?
A. 12 V2.2 B. 8. 13:39 C. 6. 74.23
D. 3. 16:23
(Zadanie w załączniku jak coś ) zad 8

[tex]A. \ 12\cdot\sqrt[3]{2}\cdot2^{\frac{3}{4}}=12\cdot2^{\frac{1}{3}}\cdot2^{\frac{3}{4}} = 12\cdot2^{\frac{1}{3}+\frac{3}{4}} = 12\cdot2^{\frac{13}{12}}\neq 24\\\\B. \ 8\cdot\sqrt{3}\cdot3^{\frac{3}{2}} =8\cdot\sqrt{3}\cdot\sqrt{3^{3}} = 8\cdot\sqrt{3\cdot3^{3}} =8\cdot\sqrt{3^{4}} = 8\cdot3^{2} = 8\cdot9 = 72\neq 24\\\\\underline{C. \ 6\cdot\sqrt[3]{4}\cdot2^{\frac{4}{3}} = 6\cdot\sqrt[3]{4}\cdot\sqrt[3]{2^{4}}=6\cdot\sqrt[3]{4}\cdot\sqrt[3]{16} = 6\cdot\sqrt[3]{4\cdot16} = 6\sqrt[3]{64} = 6\cdot4 = 24}[/tex]

[tex]D. \ 3\cdot\sqrt{6}\cdot2^{\frac{3}{2}}=3\cdot\sqrt{6}\cdot\sqrt{2^{3}} = 3\cdot\sqrt{6\cdot8} = 3\cdot\sqrt{48} = 3\cdot\sqrt{16\cdot3} = 3\cdot4\cdot\sqrt{3} =12\sqrt{3}\neq 24[/tex]

Mutopompkaviz Mutopompkaviz · Answer 2

Odpowiedź i szczegółowe wyjaśnienie:

[tex]a)\ 12\cdot\sqrt[3]2\cdot2^\frac34=12\cdot2^\frac13\cdot2^\frac34=12\cdot2^{\frac13+\frac34}}=12\cdot2^{\frac{4}{12}+\frac{9}{12}}=12\cdot2^{\frac{13}{12}}=\\\\=12\cdot2\cdot2^\frac{1}{12}=24\cdot\sqrt[12]2\\\\b)\ 8\cdot \sqrt3\cdot3^\frac32=8\cdot3^\frac12\cdot3^\frac32=8\cdot3^{\frac12+\frac32}=8\cdot3^{\frac42}=8\cdot3^2=8\cdot9=72\\\\c)\ 6\cdot \sqrt[3]4\cdot2^\frac43=6\cdot4^\frac13\cdot2^\frac43=6\cdot2^\frac23\cdot2^\frac43=6\cdot2^{\frac23+\frac43}=6\cdot2^2=6\cdot 4=24\\\\[/tex]

[tex]d)\ 3\cdot \sqrt6\cdot2^\frac32=3\cdot\sqrt{3\cdot2}\cdot2^\frac32=3\sqrt3\cdot2^\frac12\cdot2^\frac32=3\sqrt3\cdot2^{\frac12+\frac32}=\\\\=3\sqrt3\cdot2^2=3\sqrt3\cdot4=12\sqrt3[/tex]