Question

rationalize the denominator involute root 2÷ 2 + root 2 by taking root 2 equals to 1.414 upto 3 decimal places

Answer 1

$\frac{ \sqrt{2} }{2 + \sqrt{2} } \\ = \frac{ \sqrt{2}(2 - \sqrt{2}) }{(2 + \sqrt{2}) (2 - \sqrt{2} )} \\ = \frac{2 \sqrt{2} - 2 }{ {2}^{2} - { \sqrt{2 } }^{2} } \\ = \frac{2( \sqrt{2} - 1) }{4 - 2} \\ = \frac{2( \sqrt{2} - 1)}{2} \\ = \sqrt{2} - 1 \\ = 1.414 - 1 \\ = 0.414$
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