rasionalkan penyebut pecahan-pecahan berikut a. 3/√5b. 15/√7c.2√2/6√6d. 16√100/1+√32e. 10/5-√2f. 2√5/√3+√5g. 15/√11-√8h. 2√5+2√3/2√5-2-√3
Matematika
mfarhanrizkyandi
Pertanyaan
rasionalkan penyebut pecahan-pecahan berikut a. 3/√5b. 15/√7c.2√2/6√6d. 16√100/1+√32e. 10/5-√2f. 2√5/√3+√5g. 15/√11-√8h. 2√5+2√3/2√5-2-√3
1 Jawaban
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1. Jawaban AlfandyGulo
a.
[tex] = \frac{3}{ \sqrt{5} } \times \frac{ \sqrt{5} }{ \sqrt{5} } \\ = \frac{3}{5} \sqrt{5} [/tex]
b.
[tex] = \frac{15}{ \sqrt{7} } \times \frac{ \sqrt{7} }{ \sqrt{7} } \\ = \frac{15}{7} \sqrt{7} [/tex]
c.
[tex] = \frac{2 \sqrt{2} }{6 \sqrt{6} } \\ = \frac{ \sqrt{2} }{3 \sqrt{6} } \times \frac{3 \sqrt{6} }{3 \sqrt{6} } \\ = \frac{3 \sqrt{12} }{9 \times 6} \\ = \frac{6 \sqrt{2} }{54} \\ = \frac{1}{9} \sqrt{2} [/tex]
d.
[tex] = \frac{6 \sqrt{100} }{1 + \sqrt{32} } \\ = \frac{60}{1 + 4 \sqrt{2} } \\ = \frac{60}{1 + 4 \sqrt{2} } \times \frac{1 - 4 \sqrt{2} }{1 - 4 \sqrt{2} } \\ = \frac{60 - 240 \sqrt{2} }{1 - 32} \\ = - \frac{60}{31} + \frac{240}{31} \sqrt{2} [/tex]