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

1 Answer
Johnson Z.
Mar 28, 2016

#6-3sqrt(3)#

Explanation:

#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)|)))#

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