Penjelasan dengan langkah-langkah:
[tex]14. \: \: \frac{2 \sqrt{54} + 4 \sqrt{6} }{4 \sqrt{8} - 3 \sqrt{2} } \\ = \frac{2 \sqrt{9 \times 6} + 4 \sqrt{6} }{4 \sqrt{4 \times 2} - 3 \sqrt{2} } \\ = \frac{2 \times 3 \sqrt{6} + 4 \sqrt{6} }{4 \times 2 \sqrt{2} - 3 \sqrt{2} } \\ = \frac{6 \sqrt{6} + 4 \sqrt{6} }{8 \sqrt{2} - 3 \sqrt{2} } \\ = \frac{10 \sqrt{6} }{5 \sqrt{2} } \\ = \frac{2 \sqrt{6} }{ \sqrt{2} } \\ = \frac{2 \sqrt{6} }{ \sqrt{2} } \times \frac{ \sqrt{2} }{ \sqrt{2} } \\ = \frac{2 \sqrt{12} }{( \sqrt{ {2}^{} } ) {}^{2} } \\ = \frac{2 \sqrt{4 \times 3} }{2} \\ = \sqrt{4 \times 3} \\ = 2 \sqrt{3} [/tex]
[tex]15. \: \: \frac{4 \sqrt{18} - 6 \sqrt{6} }{3 \sqrt{2} + 2 \sqrt{6} } \\ = \frac{4 \sqrt{9 \times 2} - 6 \sqrt{3 \times 2} }{3 \sqrt{2} + 2 \sqrt{3\times 2} } \\ = \frac{4 \times 3 \sqrt{2} - 6 \sqrt{3} \times \sqrt{2} }{3 \sqrt{2} + 2 \sqrt{3} \times \sqrt{2} } \\ = \frac{12 - 6 \sqrt{3} }{3 + 2 \sqrt{3} } \times \frac{3 - 2 \sqrt{3} }{3 - 2 \sqrt{3} } \\ = \frac{36 - 24 \sqrt{3} - 18 \sqrt{3} + 12 \times 3}{9 - 4 \times 3} \\ = \frac{72 - 42 \sqrt{3} }{ - 3} \\ = - 24 + 14 \sqrt{3} [/tex]
[tex]16. \: \: 0,0000002156 \\ = \frac{2156}{10000000000} \\ = \frac{2156}{10 {}^{10} } \\ = \frac{2,156}{ {10}^{7} } \\ = 2,156 \times {10}^{ - 7} [/tex]
[tex]17. \: \: k = \sqrt{200} \: cm \\ p = \sqrt{18} \: cm \\ k = 2p + 2l[/tex]
[tex]jadi, \\ k = 2p + 2l \\ \sqrt{200} = 2 \times \sqrt{18} + 2l \\ \sqrt{100 \times 2} = 2 \times \sqrt{9 \times 2} + 2l \\ 10 \sqrt{2 } = 2 \times 3 \sqrt{2} + 2l \\ 10 \sqrt{2} = 6 \sqrt{2} + 2l \\ 10 \sqrt{2} - 6 \sqrt{2} = 2l \\ 4 \sqrt{2} = 2l \\ l = \frac{4 \sqrt{2} }{2} \\ = 2 \sqrt{2 \: } cm[/tex]
Semoga membantu ya ;)
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Penjelasan dengan langkah-langkah:
[tex]14. \: \: \frac{2 \sqrt{54} + 4 \sqrt{6} }{4 \sqrt{8} - 3 \sqrt{2} } \\ = \frac{2 \sqrt{9 \times 6} + 4 \sqrt{6} }{4 \sqrt{4 \times 2} - 3 \sqrt{2} } \\ = \frac{2 \times 3 \sqrt{6} + 4 \sqrt{6} }{4 \times 2 \sqrt{2} - 3 \sqrt{2} } \\ = \frac{6 \sqrt{6} + 4 \sqrt{6} }{8 \sqrt{2} - 3 \sqrt{2} } \\ = \frac{10 \sqrt{6} }{5 \sqrt{2} } \\ = \frac{2 \sqrt{6} }{ \sqrt{2} } \\ = \frac{2 \sqrt{6} }{ \sqrt{2} } \times \frac{ \sqrt{2} }{ \sqrt{2} } \\ = \frac{2 \sqrt{12} }{( \sqrt{ {2}^{} } ) {}^{2} } \\ = \frac{2 \sqrt{4 \times 3} }{2} \\ = \sqrt{4 \times 3} \\ = 2 \sqrt{3} [/tex]
[tex]15. \: \: \frac{4 \sqrt{18} - 6 \sqrt{6} }{3 \sqrt{2} + 2 \sqrt{6} } \\ = \frac{4 \sqrt{9 \times 2} - 6 \sqrt{3 \times 2} }{3 \sqrt{2} + 2 \sqrt{3\times 2} } \\ = \frac{4 \times 3 \sqrt{2} - 6 \sqrt{3} \times \sqrt{2} }{3 \sqrt{2} + 2 \sqrt{3} \times \sqrt{2} } \\ = \frac{12 - 6 \sqrt{3} }{3 + 2 \sqrt{3} } \times \frac{3 - 2 \sqrt{3} }{3 - 2 \sqrt{3} } \\ = \frac{36 - 24 \sqrt{3} - 18 \sqrt{3} + 12 \times 3}{9 - 4 \times 3} \\ = \frac{72 - 42 \sqrt{3} }{ - 3} \\ = - 24 + 14 \sqrt{3} [/tex]
[tex]16. \: \: 0,0000002156 \\ = \frac{2156}{10000000000} \\ = \frac{2156}{10 {}^{10} } \\ = \frac{2,156}{ {10}^{7} } \\ = 2,156 \times {10}^{ - 7} [/tex]
[tex]17. \: \: k = \sqrt{200} \: cm \\ p = \sqrt{18} \: cm \\ k = 2p + 2l[/tex]
[tex]jadi, \\ k = 2p + 2l \\ \sqrt{200} = 2 \times \sqrt{18} + 2l \\ \sqrt{100 \times 2} = 2 \times \sqrt{9 \times 2} + 2l \\ 10 \sqrt{2 } = 2 \times 3 \sqrt{2} + 2l \\ 10 \sqrt{2} = 6 \sqrt{2} + 2l \\ 10 \sqrt{2} - 6 \sqrt{2} = 2l \\ 4 \sqrt{2} = 2l \\ l = \frac{4 \sqrt{2} }{2} \\ = 2 \sqrt{2 \: } cm[/tex]
Semoga membantu ya ;)