Question

Find the value of 1/1+√2
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Answer 1

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Find the value of 1/1+√2

$\huge\tt{\bold{\underline{\underline{Answer᎓}}}}$

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$\bold{= > \frac{1}{1 + \sqrt{2} }}$

=>Here,we Rationalise the terms by multiplying both numerator and denominator with opposite signs of denominator.

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

=>Here,this identity is used:-

$\bold{ = > {x}^{2} - {y}^{2} = (x + y)(x - y)}$

$\bold{= > \frac{1 - \sqrt{2} }{ {(1)}^{2} - {( \sqrt{2}) }^{2} }}$

$\bold{= > \frac{1 - \sqrt{2} }{1 - 2}}$

$\bold{ = > \frac{1 - \sqrt{2} }{ - 1} = \frac{ - ( \sqrt{2} - 1) }{ - 1}}$

$\bold{\boxed{\red{ = > \sqrt{2} - 1}}}$

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