How do you rationalize the denominator and simplify #2/(5-sqrt3)#?

1 Answer
Mar 28, 2016

Answer:

#(5+sqrt(3))/11#

Explanation:

#1#. Multiply the numerator and denominator by the conjugate of #5-sqrt(3)#, which is #5+sqrt(3)#.

#2/(5-sqrt(3))#

#=2/(5-sqrt(3))((5+sqrt(3))/(5+sqrt(3)))#

#2#. Simplify the numerator.

#=(10+2sqrt(3))/((5-sqrt(3))(5+sqrt(3))#

#3#. Simplify the denominator.

#=(10+2sqrt(3))/(25-3)#

#=(10+2sqrt(3))/22#

#4#. Factor out #2# from the numerator and denominator.

#=(2(5+sqrt(3)))/(2(11))#

#=(color(red)cancelcolor(black)2(5+sqrt(3)))/(color(red)cancelcolor(black)2(11))#

#=color(green)(|bar(ul(color(white)(a/a)(5+sqrt(3))/11color(white)(a/a)|)))#