Question

Rationalise the denominator of
$\frac{1}{1 + \sqrt{2} }$
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Answer 1

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

$\frac{1}{1 + \sqrt{2} } \\ = \frac{1}{1 + \sqrt{2} } \times \frac{1 - \sqrt{2} }{1 - \sqrt{2} } \\ = \frac{1 - \sqrt{2} }{ {1}^{2} - { \sqrt{2} }^{2} } \\ = \frac{1 - \sqrt{2} }{1 - 2} \\ = \frac{1 - \sqrt{2} }{ - 1} \\ = \sqrt{2} - 1$