Question

simplify the question 1/1+√2​

Answer 1

⚕️ Question :-

Simplify the question :-$\frac{1}{1 + \sqrt{2} }$

⚕️ Solution :-

Rationalise the denominator :-

$\implies \frac{1}{1+ \sqrt{2} } \times \frac{1 - \sqrt{2} }{1- \sqrt{2} }$

We have to use the identity a² - b² = ( a-b ) ( a+b ) :-

$\implies \frac{1 - \sqrt{2} }{(1)²-( \sqrt{2)} ²}$

$\implies \frac{1 - \sqrt{2} }{1-2}$

$\implies \frac{1 - \sqrt{2} }{-1}$

$\implies \small - (1 - \sqrt{2)}$

$\implies\small -1 + \sqrt{2}$

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