Question

Rationalise the denominator of 1/2+√3.​

Answer 1

Answer:

Hey!! Ur answer:

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

Step-by-step explanation:

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Answer 2

⠀⌬⠀ Rationalise the Denominator of :

$\qquad \qquad \bigstar \sf \:\:\dfrac{1}{2\:+\:\sqrt{3}}\:\:$

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━⠀

$\qquad \dashrightarrow \sf \:\:\dfrac{1}{2\:+\:\sqrt{3}}\:\:$

⠀⠀▪︎ In order to Rationalise the Denominator we've to Multiply it's both numerator and denominator by it's Rationalising Factor , & The Rationalising factor of Given is ( 2 - √3 ) .

$\qquad \bigstar \:\:\underline {\purple {\pmb{\sf \:By\:Multiplying \:both\:the \:Numerator \:and\:\:Denominator \:by \: \: \big( 2 -\sqrt{3}\:\big) \::\:}}}$

$\qquad \dashrightarrow \sf \:\:\dfrac{\big( 2 -\sqrt{3}\:\big)}{2\:+\:\sqrt{3}}\:\:\\\\\\ \qquad \dashrightarrow \sf \:\:\dfrac{1\: \big( 2 -\sqrt{3}\:\big)}{\big( 2 +\sqrt{3}\:\big)\:\big( 2 -\sqrt{3}\:\big)\:}\:\:\\\\ \\ \qquad \dashrightarrow \sf \:\:\dfrac{\big( 2 -\sqrt{3}\:\big)}{\big( 2 +\sqrt{3}\:\big)\:\big( 2 -\sqrt{3}\:\big)\:}\:\:\\\\ \\ \qquad \dashrightarrow \sf \:\:\dfrac{ 2 -\sqrt{3}\:}{\big( 2\big)^2 - \big( \sqrt{3}\:\big)^2\:\:\big)\:}\:\:\qquad \because \:\bigg\lgroup \sf{ \:(\:a^2\:-\:b^2\:)\:=\:( a + b ) \:( a - b ) }\bigg\rgroup\\\\ \\ \qquad \dashrightarrow \sf \:\:\dfrac{ 2 -\sqrt{3}\:}{4 - \:\:3\:}\:\:\\\\ \\ \qquad \dashrightarrow \sf \:\:\dfrac{ 2 -\sqrt{3}\:}{\:1\:}\:\:\\\\ \\ \qquad \dashrightarrow \sf \:\:\underline {\boxed{\pmb{\frak{\purple { Rationalised\:Form\:=\: 2-\sqrt{3}\:}}}}}\:\:\bigstar$

$\therefore \:\sf \:\underline { Hence, \:The \:Rationalised \:form \:is \: \pmb{\bf 2 - \sqrt{3}\:\:}\:.}$