Rasionalkan bentuk akar berikut
[tex] \frac{4}{3 + \sqrt{2} } [/tex]
[tex] = \frac{4}{3 + \sqrt{2} } \times \frac{3 - \sqrt{2} }{3 - \sqrt{2} } [/tex]
[tex] = \frac{4(3 - \sqrt{2} )}{(3 + \sqrt{2}) \times (3 - \sqrt{2} ) } [/tex]
[tex] = \frac{12 - 4 \sqrt{2} }{9 - 2} [/tex]
[tex] = \frac{12 - 4 \sqrt{2} }{7} [/tex]
[tex]\frac{4}{3 + \sqrt{2}} = \frac{4}{3 + \sqrt{2}} \times \frac{3 - \sqrt{2}}{3 - \sqrt{2}} = \frac{(4)(3 - \sqrt{2})}{(3 + \sqrt{2})(3 - \sqrt{2})} [/tex]
[tex]= \frac{12 - 4 \sqrt{2}}{9 - 3 \sqrt{2} + 3 \sqrt{2} - \sqrt{4}} [/tex]
[tex]= \frac{12 - 4 \sqrt{2}}{9 - \sqrt{4}} = \frac{12 - 4 \sqrt{2}}{9 - 2} = \frac{12 - 4 \sqrt{2}}{7} [/tex]
[answer.2.content]
