Question

Rationalise the denominator of 3 + root6 / 3- root6

Answer 1

Answer:

$\frac{3 + \sqrt{6} }{3 - \sqrt{6} } = \frac{3 + \sqrt{6} }{3 - \sqrt{6} } \times \frac{3 + \sqrt{6} }{3 + \sqrt{6} } \\ = \frac{ {(3 + \sqrt{6)} }^{2} }{ { \sqrt{3} }^{2} - { \sqrt{6} }^{2} } \\ = \frac{9 + 6 + 2 \times 3 \times \sqrt{6} }{3 - 6} \\ = \frac{15 + 6 \sqrt{6} }{ - 3} \\ = - 3( - 5 - 2 \sqrt{3)} \div - 3 \\ = - (5 + 2 \sqrt{3)}$