Question

Rationalise the denominator of 5+root 3 / 3+root 6​

Answer 1

Step-by-step explanation:

$= \frac{5 + \sqrt{3} }{3 + \sqrt{6} } \\ = \frac{5 + \sqrt{3} }{3 + \sqrt{6} } \times \frac{3 - \sqrt{6}}{3 - \sqrt{6}} \\ = \frac{(5 + \sqrt{3})(3 - \sqrt{6})}{ {(3)}^{2} - { (\sqrt{6}) }^{2} } \\ = \frac{15 - 5 \sqrt{6} + 3 \sqrt{3} - \sqrt{18} }{9 - 6} \\ = \frac{15 - 5 \sqrt{6} + 3 \sqrt{3} - \sqrt{3 \times 3 \times 2} }{3} \\ = \frac{15 - 5 \sqrt{6} + 3 \sqrt{3} - 3 \sqrt{2} }{3}$

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