Question

rationalise the denominator of 1/√(√2 + 1)

Answer 1

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Answer 2

Step-by-step explanation:

$\bf \underline{Solution-}$

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

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

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

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

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

$\bf = \sqrt{2} - 1$