Question

rationalize 3-2√2/5+6√3​

Answer 1

$\frac{3 - 2 \sqrt{2} }{5 + 6 \sqrt{3} } \\ = \frac{3 - 2 \sqrt{2} }{5 + 6 \sqrt{3} } \times \frac{5 - 6 \sqrt{3}}{5 - 6 \sqrt{3}} \\ = \frac{15 - 18 \sqrt{3 } - 10 \sqrt{2} + 12 \sqrt{6} }{ {(5})^{2} - ({6 \sqrt{3} )}^{2} } \\ =\frac{15 - 18 \sqrt{3 } - 10 \sqrt{2} + 12 \sqrt{6} }{ 25 - 108 } \\ = \frac{15 - 18 \sqrt{3 } - 10 \sqrt{2} + 12 \sqrt{6} }{ - 83 }$