Question

Please tell me details plz ​

Answer 1

${\large{\pmb{\sf{\underline{RequirEd \; Solution...}}}}}$

${\bigstar \:{\pmb{\sf{\underline{Understanding \: the \: question...}}}}}$

⋆ This question says that we have to rationalize the denominator of the given expression. Let the rationalize the denominator, let's solve this question!

${\bigstar \:{\pmb{\sf{\underline{Given \: that...}}}}}$

${\sf{\star \: Rationalize \: denominator \: of \: \dfrac{\sqrt{2}}{\sqrt{2}-1}}}$

${\bigstar \:{\pmb{\sf{\underline{What \: to \: do...}}}}}$

${\sf{\star \: Rationalize \: the \: denominator \: of \: given \: expression}}$

${\bigstar \:{\pmb{\sf{\underline{Solution...}}}}}$

${\sf{\star \: By \: rationalising \: we \: get \: \bf{3} \: \sf as \: solution}}$

${\bigstar \:{\pmb{\sf{\underline{Using \: concept...}}}}}$

${\sf{\star \: An \: algebraic \: standard \: identity}}$

${\bigstar \:{\pmb{\sf{\underline{Using \: identity...}}}}}$

${\sf{\star \: Using \: identity \: = \bf{(a-b)(a+b) = a^2 - b^2}}}$

${\bigstar \:{\pmb{\sf{\underline{Full \; Solution...}}}}}$

$:\implies \sf Rationalize \: denominator \: of \: \dfrac{\sqrt{2}}{\sqrt{2}-1} \\ \\ :\implies \sf \dfrac{\sqrt{2}}{\sqrt{2}-1} \\ \\ :\implies \sf \dfrac{\sqrt{2}}{\sqrt{2}-1} \times \dfrac{\sqrt{2}+1}{\sqrt{2}+1} \\ \\ \sf Now \: we \: have \: to \: use \: identity \\ \\ \sf \leadsto (a-b)(a+b) = a^2 - b^2 \\ \\ \sf According \: to \: the \: identity \\ \\ \sf Here, \: a \: is \: \sqrt{2} \: and \: b \: is \: 1 \\ \\ \sf By \: using \: identity \: we \: get \: (denominator) \\ \\ :\implies \sf (\sqrt{2})^{2} - (1)^{2} \\ \\ :\implies \sf (\cancel{\sqrt{2}})^{ \cancel{2}} - (1)^{2} \\ \\ :\implies \sf 2 - 1 \\ \\ :\implies \sf 1 \\ \\ \sf Now \: let's \: carry \: on \\ \\ :\implies \sf \dfrac{2+1}{1} \\ \\ :\implies \sf \dfrac{3}{1} \\ \\ :\implies \sf 3 \: is \: requied \: solution \\ \\ {\pmb{\sf{Henceforth, \: rationalize!!}}}$