Question

Simplify 1 + root2 by 2-root2

Answer 1

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$\frac{1 + \sqrt{2} }{2 - \sqrt{2} } \times \frac{2 + \sqrt{2} }{2 + \sqrt{2} } \\ \\ \frac{(1 + \sqrt{2} )(2 + \sqrt{2} )}{ ({2})^{2} - { (\sqrt{2} )}^{2} } \\ \\ \frac{1(2 + \sqrt{2} ) + \sqrt{2} (2 + \sqrt{2}) }{4 - 2} \\ \\ \frac{2 + \sqrt{2} + 2 \sqrt{2} + { (\sqrt{2} )}^{2} }{2} \\ \\ \frac{2 + 3 \sqrt{2} + 2}{2} \\ \\ \frac{4 + 3 \sqrt{2} }{2}$