pake caranya ya kak
Nomor 1
[tex]5 \sqrt{3} + 10 \sqrt{3} \\ = (5 + 10) \sqrt{3} \\ = 15 \sqrt{3} [/tex]
[tex] \\ [/tex]
Nomor 2
[tex]5 \sqrt{12} - 2 \sqrt{3} \\ = 5 \sqrt{4 \times 3} - 2 \sqrt{3} \\ = 5 \times 2 \sqrt{3} - 2 \sqrt{3} \\ = 10 \sqrt{3} - 2 \sqrt{3} \\ = (10 - 2) \sqrt{3} \\ = 8 \sqrt{3} [/tex]
[tex] \\ [/tex]
Nomor 3
[tex]5 \sqrt{3} + \sqrt{48} - 2 \sqrt{27} \\ = 5 \sqrt{3} + \sqrt{16 \times 3} - 2 \sqrt{9 \times 3} \\ = 5 \sqrt{3} + 4 \sqrt{3} - 2 \times 3 \sqrt{3} \\ = 5 \sqrt{3} + 4 \sqrt{3} - 6 \sqrt{3} \\ = (5 + 4 - 6) \sqrt{3} \\ = 3 \sqrt{3} [/tex]
[tex] \\ [/tex]
Nomor 4
[tex]5 \sqrt{2} + \sqrt{14} - 3 \sqrt{2} \\ = (5 - 3) \sqrt{2} + \sqrt{14} \\ = 2 \sqrt{2} + \sqrt{14} [/tex]
[tex] \\ [/tex]
Nomor 5
[tex]2 \sqrt{20} - \sqrt{45} - 7 \sqrt{5} - \sqrt{20} \\ = 2 \sqrt{4 \times 5} - \sqrt{9 \times 5} - 7 \sqrt{5} - \sqrt{4 \times 5} \\ = 2 \times 2 \sqrt{5} - 3 \sqrt{5} - 7 \sqrt{5} - 2 \sqrt{5} \\ = 4 \sqrt{5} - 3 \sqrt{5} - 7 \sqrt{5} - 2 \sqrt{5} \\ = (4 - 3 - 7 - 2) \sqrt{5} \\ = - 10 \sqrt{5} [/tex]
[tex] \\ [/tex]
Nomor 6
[tex]4 \sqrt{7} - \sqrt{28} - \sqrt{63} + 5 \sqrt{28} \\ = 4 \sqrt{7} - \sqrt{4 \times 7} - \sqrt{9 \times 7} + 5 \sqrt{4 \times 7} \\ = 4 \sqrt{7} - 2 \sqrt{7} - 3 \sqrt{7} + 10 \sqrt{7} \\ = (4 - 2 - 3 + 10) \sqrt{7} \\ = 9 \sqrt{7} [/tex]
[tex] \\ [/tex]
Nomor 7
[tex]2 \sqrt{12} - 5 \sqrt{3} \\ = 2 \sqrt{4 \times 3} - 5 \sqrt{3} \\ = 2 \times 2 \sqrt{3} - 5 \sqrt{3} \\ = 4 \sqrt{3} - 5 \sqrt{3} \\ (4 - 5) \sqrt{3} \\ = - 1 \sqrt{3} \\ = - \sqrt{3} [/tex]
[tex] \\ [/tex]
Nomor 8
[tex] \sqrt{96} - 3 \sqrt{24} \\ = \sqrt{16 \times 6} - 3 \sqrt{4 \times 6} \\ = 4 \sqrt{6} - 3 \times 2 \sqrt{6} \\ = 4 \sqrt{6} - 6 \sqrt{6} \\ = (4 - 6) \sqrt{6} \\ = - 2 \sqrt{6} [/tex]
[tex] \\ [/tex]
Nomor 9
[tex] \sqrt{6 } \times \sqrt{3} \\ = \sqrt{6 \times 3} \\ = \sqrt{18} \\ = \sqrt{9 \times 2} \\ = 3 \sqrt{2} [/tex]
[tex] \\ [/tex]
Nomor 10
[tex] \sqrt{11} \times \sqrt{3} \\ = \sqrt{11 \times 3} \\ = \sqrt{33} [/tex]
[tex] \\ [/tex]
Nomor 11
[tex] \sqrt[5]{4} \times \sqrt[5]{7} \\ = \sqrt[5]{4 \times 7} \\ = \sqrt[5]{28} [/tex]
[tex] \\ [/tex]
Nomor 12
[tex] \sqrt{5} ( \sqrt{2} + 4) \\ = ( \sqrt{5} \times \sqrt{2} ) + ( \sqrt{5} \times 4) \\ = \sqrt{10} + 4 \sqrt{5} [/tex]
[tex] \\ [/tex]
Nomor 13
[tex]( \sqrt{3} + \sqrt{5} )( \sqrt{5} - \sqrt{2} ) \\ \small{= ( \sqrt{3} \times \sqrt{5} ) + ( \sqrt{3} \times ( - \sqrt{2} ) + ( \sqrt{5} \times \sqrt{5} ) + ( \sqrt{5 } \times ( - \sqrt{2} )} \\ = \sqrt{15} - \sqrt{6} + 5 - \sqrt{10} [/tex]
[tex] \\ [/tex]
Nomor 14
[tex] \sqrt{8} \div \sqrt{2} \\ = \sqrt{8 \div 2} \\ = \sqrt{4} \\ = 2[/tex]
Jawaban:
1.
[tex]5 \sqrt{3} + 10 \sqrt{3} = (10 + 5) \sqrt{3} = 15 \sqrt{3} [/tex]
2.
[tex]5 \sqrt{12} - 2 \sqrt{3} = 5 \sqrt{3 \times 4} - 2 \sqrt{3} = 10 \sqrt{3} - 2 \sqrt{3} = 8 \sqrt{3} [/tex]
3.
[tex]5 \sqrt{3} + \sqrt{48} - 2 \sqrt{27} = 5 \sqrt{3} + \sqrt{3 \times 16} - 2 \sqrt{3 \times 9} = 5 \sqrt{3} + 4 \sqrt{3} - 6 \sqrt{3} = 3 \sqrt{3} [/tex]
4.
[tex]5 \sqrt{2} + \sqrt{14} - 3 \sqrt{2} = 2 \sqrt{2} + \sqrt{14} [/tex]
5.
[tex]2 \sqrt{20} - \sqrt{45} - 7 \sqrt{5} - \sqrt{20} = 2 \sqrt{5 \times 4} - \sqrt{5 \times 9} - 7 \sqrt{5} - \sqrt{5 \times 4} = 4 \sqrt{5} - 3 \sqrt{5} - 7 \sqrt{5} - 2 \sqrt{5} = - 8 \sqrt{5} [/tex]
6.
[tex]4 \sqrt{7} - \sqrt{28} - \sqrt{63} +5 \sqrt{28} = 4 \sqrt{7} - \sqrt{7 \times 4} - \sqrt{7 \times 9} + 5 \sqrt{7 \times 4} = 4 \sqrt{7} - 2 \sqrt{7} - 3 \sqrt{7} + 10 \sqrt{7} = 9 \sqrt{7} [/tex]
7.
[tex]2 \sqrt{12} - 5 \sqrt{3} = 2 \sqrt{ 3\times 4} - 5 \sqrt{3} = 4 \sqrt{3} - 5 \sqrt{3} = - \sqrt{3} [/tex]
8.
[tex] \sqrt{96} - 3 \sqrt{24} = \sqrt{6 \times 16} - 3 \sqrt{6 \times 4} = 4 \sqrt{6} - 6 \sqrt{6} = - 2 \sqrt{6} [/tex]
9.
[tex] \sqrt{6} \times \sqrt{3} = \sqrt{(6 \times 3)} = \sqrt{18} = \sqrt{2 \times 9} = 3 \sqrt{2} [/tex]
10.
[tex] \sqrt{11} \times \sqrt{3} = \sqrt{11 \times 3} = \sqrt{33} [/tex]
11.
[tex] \sqrt[5]{4} \times \sqrt[5]{7} = \sqrt[5]{4 \times 7} = \sqrt[5]{28} [/tex]
12.
[tex] \sqrt{5} ( \sqrt{2} + 4) = ( \sqrt{5} \times \sqrt{2} ) + ( \sqrt{5} \times 4) = \sqrt{10} + 4 \sqrt{5} [/tex]
13.
[tex]( \sqrt{3} + \sqrt{5} )( \sqrt{5} - \sqrt{2)} = ( \sqrt{3} \times \sqrt{5} ) + ( - \sqrt{2} \times \sqrt{3} ) + ( \sqrt{5} \times \sqrt{5} ) + ( \sqrt{5} \times - \sqrt{2} ) = \sqrt{15} - \sqrt{6} + 5 - \sqrt{10} = \sqrt{15} - \sqrt{10} - \sqrt{6} + 5[/tex]
14.
[tex] \sqrt{8} \div \sqrt{2} = \sqrt{8 \div 2} = \sqrt{4} = 2[/tex]
jadikan jawaban tercerdas ya
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