V8+V7/ 4V3+V6V15+V25/2V3-V2​

NOMOR 1.

[tex]\frac{\sqrt{8} + \sqrt{7}}{4 \sqrt{3} + \sqrt{6}} = \frac{\sqrt{4 \times 2} + \sqrt{7}}{4 \sqrt{3} + \sqrt{6}} = \frac{2 \sqrt{2} + \sqrt{7}}{4 \sqrt{3} + \sqrt{6}} [/tex]

Kemudian merasionalkan penyebutnya, sehingga :

[tex]\frac{2 \sqrt{2} + \sqrt{7}}{4 \sqrt{3} + \sqrt{6}} = \frac{2 \sqrt{2} + \sqrt{7}}{4 \sqrt{3} + \sqrt{6}} \times \frac{4 \sqrt{3} - \sqrt{6}}{4 \sqrt{3} - \sqrt{6}} [/tex]

[tex]= \frac{(2 \sqrt{2} + \sqrt{7})(4 \sqrt{3} - \sqrt{6})}{(4 \sqrt{3} + \sqrt{6})(4 \sqrt{3} - \sqrt{6})} [/tex]

[tex]= \frac{8 \sqrt{6} - 2 \sqrt{12} + 4 \sqrt{21} - \sqrt{42}}{16 \sqrt{9} - 4 \sqrt{18} + 4 \sqrt{18} - \sqrt{36}} [/tex]

[tex]= \frac{8 \sqrt{6} - 2 \sqrt{4 \times 3} + 4 \sqrt{21} - \sqrt{42} }{16 \sqrt{9} - \sqrt{36}} [/tex]

[tex]= \frac{8 \sqrt{6} - 2 \times 2 \sqrt{3} + 4 \sqrt{21} - \sqrt{42}}{16 \times 3 - 6} [/tex]

[tex]= \frac{8 \sqrt{6} - 4 \sqrt{3} + 4 \sqrt{21} - \sqrt{42}}{48 - 6} = \frac{8 \sqrt{6} - 4 \sqrt{3} + 4 \sqrt{21} - \sqrt{42}}{42}[/tex]

NOMOR 2.

[tex]\frac{\sqrt{15} + \sqrt{25}}{2 \sqrt{3} - \sqrt{2}} = \frac{\sqrt{15} + 5}{2 \sqrt{3} - \sqrt{2}}[/tex]

Kemudian merasionalkan penyebutnya, sehingga :

[tex]\frac{\sqrt{15} + 5}{2 \sqrt{3} - \sqrt{2}} = \frac{\sqrt{15} + 5}{2 \sqrt{3} - \sqrt{2}} \times \frac{2 \sqrt{3} + \sqrt{2}}{2 \sqrt{3} + \sqrt{2}} [/tex]

[tex]= \frac{(\sqrt{15} + 5)(2 \sqrt{3} + \sqrt{2})}{(2 \sqrt{3} - \sqrt{2})(2 \sqrt{3} + \sqrt{2})} [/tex]

[tex]= \frac{2 \sqrt{45} + \sqrt{30} + 10 \sqrt{3} + 5 \sqrt{2}}{4 \sqrt{9} + 2 \sqrt{6} - 2 \sqrt{6} - \sqrt{4}} [/tex]

[tex]= \frac{2 \sqrt{9 \times 5} + \sqrt{30} + 10 \sqrt{3} + 5 \sqrt{2}}{4 \sqrt{9} - \sqrt{4}} [/tex]

[tex]= \frac{2 \times 3 \sqrt{5} + \sqrt{30} + 10 \sqrt{3} + 5 \sqrt{2}}{4 \times 3 - 2} [/tex]

[tex]= \frac{6 \sqrt{5} + \sqrt{30} + 10 \sqrt{3} + 5 \sqrt{2}}{12 - 2} = \frac{6 \sqrt{5} + \sqrt{30} + 10 \sqrt{3} + 5 \sqrt{2}}{10} [/tex]