Question

Rationalize the denominator of 1/3-√2​

Answer 1

Solution :

$\frac{1}{3 - \sqrt{2} } \times \frac{3 + \sqrt{2} }{3 \ + \sqrt{2} } \\ \frac{3 + \sqrt{2} }{ {3}^{2} - ( { \sqrt{2} }^{2}) } \\ \frac{3 + \sqrt{2} }{9 - 2 } \\ \frac{3 + \sqrt{2} }{7}$

Answer 2

Answer:

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$\frac{1}{3 - \sqrt{2} } = \frac{1}{3 - \sqrt{2} } \times \frac{3 + \sqrt{2} }{3 + \sqrt{2} } \\ = \frac{3 + \sqrt{2} }{(3 + \sqrt{2)(3 - \sqrt{2} } } = \frac{3 + \sqrt{2} }{ {3}^{2} - \sqrt{ {2}^{2} } } = \frac{3 + \sqrt{2} }{9 - 2} = \frac{3 + \sqrt{2} }{7} or \frac{1}{7} (3 + \sqrt{2)}$