Question

Rationalize the denominator 1+√2 /
2-√2

Answer 1

$\huge\pink{brainliest\:plz}$ ❤️

Answer 2

Answer:

$\large\bold\red{\frac{4+3\sqrt{2}}{2}}$

Step-by-step explanation:

Given,

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

Rationalisation of Denominator

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

Niw,

we know that,

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

Therefore,

we get,

$= \frac{(1 + \sqrt{2} )(2 + \sqrt{2} )}{ {(2)}^{2} - {( \sqrt{2}) }^{2} } \\ \\ = \frac{2 + \sqrt{2} + 2 \sqrt{2} + 2}{4 - 2} \\ \\ = \frac{4 + 3 \sqrt{2} }{2}$

Hence,

Denominator is rationalised.