bentuk sederhana dari 3√2 + √7 per 2√2 - √7

Mapel : Matematika
Bab : Akar dan Pangkat

[tex] \frac{3 \sqrt{2} + \sqrt{7} }{2 \sqrt{2} - \sqrt{7} } \\ = \frac{3 \sqrt{2} + \sqrt{7} }{2 \sqrt{2} - \sqrt{7} } \times \frac{2 \sqrt{2} + \sqrt{7} }{2 \sqrt{2} + \sqrt{7} } \\ = \frac{(3 \sqrt{2} + \sqrt{7})(2 \sqrt{2} + \sqrt{7} ) }{(4 \times 2) - 7} \\ = \frac{(3 \sqrt{2} + \sqrt{7})(2 \sqrt{2} + \sqrt{7} ) }{8 - 7} \\ = \frac{(3 \sqrt{2} + \sqrt{7})(2 \sqrt{2} + \sqrt{7} )}{1} \\ = (3 \sqrt{2} + \sqrt{7} )( 2\sqrt{2} + \sqrt{7} ) \\ = 6 \sqrt{4} + 3 \sqrt{14} + 2 \sqrt{14} + 7 \\ =(6 \times 2) + 5 \sqrt{14} + 7 \\ = 12 + 5 \sqrt{14} + 7 \\ = 12 + 7 + 5 \sqrt{14} \\ = 19 + 5 \sqrt{14} [/tex]

Maaf Kalau Salah