Question

retionalize 1/(3+√2-√5)​

Answer 1

Answer:

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Answer 2

$\frac{1}{3 + \sqrt{2} - \sqrt{5} }$

$\implies \frac{(3 + \sqrt{2 }) + \sqrt{5} }{[3 + \sqrt{2} - \sqrt{5}][(3 + \sqrt{2}) + \sqrt{5} ] }$

$\implies \frac{3 + \sqrt{2 } + \sqrt{5} }{(3 + \sqrt{2} )^{2} - (\sqrt{5} )^{2} }$

$\implies \frac{3 + \sqrt{2 } + \sqrt{5} }{9 + 2 + 6 \sqrt{2} - 5 }$

$\implies \frac{3 + \sqrt{2 } + \sqrt{5} }{6 + 6 \sqrt{2} }$

$\implies \frac{3 + \sqrt{2} + \sqrt{5} }{6(1 + \sqrt{2}) }$

$\implies \frac{(3 + \sqrt{2} + \sqrt{5})(1 - \sqrt{2} ) }{6(1 + \sqrt{2})(1 - \sqrt{2} )}$

$\implies \frac{(3 + \sqrt{2} + \sqrt{5})(1 - \sqrt{2} ) }{6[(1)^{2} - (\sqrt{2}) ^{2} ]}$

$\implies \frac{3 + \sqrt{2} + \sqrt{5} - 3 \sqrt{2} - 2 - \sqrt{10}}{6[1 - 2 ]}$

$\implies \frac{1 + \sqrt{5} - 2\sqrt{2} - \sqrt{10} }{ - 6}$

$\red{\therefore \frac{ \sqrt{10} + 2 \sqrt{2} - \sqrt{5} - 1}{6} }$