Question

Please rationalize the denominator.

$\implies \dfrac{1 + \sqrt{2} }{2 - \sqrt{2} }$
Need ASAP...​

Answer 1

Question :-

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

Answer :-

$\implies \sf \dfrac{1 + \sqrt{2} }{2 - \sqrt{2} } .$

Explanation :-

As we know, to rationalize any fraction we just multiply the fraction with the fraction by changing its signs.

$\implies \sf \dfrac{1 + \sqrt{2} }{2 - \sqrt{2} } \times \dfrac{2 + \sqrt{2}}{2 + \sqrt{2} }$

$\implies \sf \dfrac{(1 + \sqrt{2})(2 + \sqrt{2}) }{(2 + \sqrt{2})( 2 - \sqrt{2} ) } .$

$\implies \sf \dfrac{2 + \sqrt{2} + 2 \sqrt{2} + 2}{(2) {}^{2} - ( \sqrt{2}) {}^{2} }$

$\bf \therefore As \: (a+b)(a-b) = a^2 - b^2$

$\implies \sf \dfrac{ 4 + 3 \sqrt{2} }{4 - 2}$

$\purple {\underline { \boxed { \bf \implies \dfrac{4 + 3 \sqrt{2} }{2} \qquad \star}}}$

Answer 2

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