How do you rationalize the denominator and simplify $3/(2+sqrt3)$ ?

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Answer 1 · 2016-03-28T03:40:24

$6-3sqrt(3)$

$1$ . Multiply the numerator and denominator by the conjugate of $2+sqrt(3)$ , which is $2-sqrt(3)$ .

$3/(2+sqrt(3))$

$=3/(2+sqrt(3))((2-sqrt(3))/(2-sqrt(3)))$

$2$ . Simplify the numerator.

$=(6-3sqrt(3))/((2+sqrt(3))(2-sqrt(3)))$

$3$ . Simplify the denominator.

$=(6-3sqrt(3))/(4-3)$

$=color(green)(|bar(ul(color(white)(a/a)6-3sqrt(3)color(white)(a/a)|)))$

How do you rationalize the denominator and simplify 3/(2+sqrt3)3/(2+sqrt3)?