2. [tex] \sqrt{ \frac{7}{5} } = \frac{ \sqrt{7} }{ \sqrt{5} } \times \frac{ \sqrt{5} }{ \sqrt{5} } = [/tex]
3. [tex] \frac{ \sqrt{2 } - 3}{2 + \sqrt{3} } \times \frac{2 - \sqrt{3} } {2 - \sqrt{3} } = [/tex]
Jawablah soal di atas beserta caranya!
NOMOR 1.
[tex]\frac{5}{\sqrt{3} - \sqrt{5}} = \frac{5}{\sqrt{3} - \sqrt{5}} \times \frac{\sqrt{3} + \sqrt{5}}{\sqrt{3} + \sqrt{5}} [/tex] [tex]= \frac{5(\sqrt{3} + \sqrt{5})}{(\sqrt{3} - \sqrt{5})(\sqrt{3} + \sqrt{5})} [/tex]
[tex]= \frac{5(\sqrt{3} + \sqrt{5})}{\sqrt{9} + \sqrt{15} - \sqrt{15} - \sqrt{25}} [/tex] [tex]= \frac{5(\sqrt{3} + \sqrt{5})}{3 + \sqrt{15} - \sqrt{15} - 5} [/tex]
[tex]= \frac{5(\sqrt{3} + \sqrt{5})}{3 - 5} = - \frac{5(\sqrt{3} + \sqrt{5})}{2} [/tex]
NOMOR 2.
[tex]\sqrt{ \frac{7}{5} } = \frac{\sqrt{7}}{\sqrt{5}} = \frac{\sqrt{7}}{\sqrt{5}} \times \frac{\sqrt{5}}{\sqrt{5}} = \frac{\sqrt{35}}{\sqrt{25}} = \frac{1}{5} \sqrt{35} [/tex]
NOMOR 3.
[tex]\frac{\sqrt{2} - 3}{2 + \sqrt{3}} = \frac{\sqrt{2} - 3}{2 + \sqrt{3}} \times \frac{2 - \sqrt{3}}{2 - \sqrt{3}} [/tex] [tex]= \frac{(\sqrt{2} - 3)(2 - \sqrt{3})}{(2 + \sqrt{3})(2 - \sqrt{3})} [/tex]
[tex]= \frac{2 \sqrt{2} - \sqrt{6} - 6 + 3 \sqrt{3}}{4 - 2 \sqrt{3} + 2 \sqrt{3} - \sqrt{9}} [/tex] [tex]= \frac{2 \sqrt{2} - \sqrt{6} - 6 + 3 \sqrt{3}}{4 - \sqrt{9}} [/tex]
[tex]= \frac{2 \sqrt{2} - \sqrt{6} - 6 + 3 \sqrt{3}}{4 - 3} [/tex] [tex]= \frac{2 \sqrt{2} - \sqrt{6} - 6 + 3 \sqrt{3}}{1} [/tex]
[tex]= 2 \sqrt{2} - \sqrt{6} + 6 + 3 \sqrt{3} [/tex]
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