Question

rationalize the denominator of the following (i) 3 + root 2/4 root 2​

Answer 1

Answer:

$\frac{3 + \sqrt{2} }{4 + \sqrt{2} } \\ \rightarrow \: \frac{3 + \sqrt{2} }{4 + \sqrt{2} } \times \frac{4 - \sqrt{2} }{4 - \sqrt{2} } \\ \rightarrow \: \frac{(3 + \sqrt{2}) (4 - \sqrt{2}) }{(4 + \sqrt{2} )(4 - \sqrt{2} )} \\ \rightarrow \: \frac{12 + 4 \sqrt{2} - 3 \sqrt{2} - 2 }{ {(4)}^{2} - { (\sqrt{2}) }^{2} } \\ \rightarrow \: \frac{12 + \sqrt{2} - 2}{16 - 2} \\ \rightarrow \: \frac{10 + \sqrt{2} }{14}$

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