How do you simplify $3/(2-sqrt3)$ ?

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Answer 1 · 2015-10-19T16:12:44

$=color(blue)(6+3sqrt3$

$3/(2-sqrt3)$

We simplify this expression by rationalisation.

We multiply both numerator and denominator by the conjugate of the denominator.

Conjugate of : $2-sqrt3= color(blue)(2+sqrt3$

$(3*color(blue)((2+sqrt3)))/((2-sqrt3)* color(blue)((2+sqrt3)$

The property :
$color(blue)((a-b)(a+b) = a^2-b^2$ , is applied to the denominator.

$(6+3sqrt3)/((2^2- (sqrt3)^2)$

$= (6+3sqrt3)/(4-3)$

$=color(blue)(6+3sqrt3$

How do you simplify 3/(2-sqrt3)3/(2-sqrt3)?