How do you rationalize the denominator and simplify #(2+ sqrt 3)/(5- sqrt 3)#?

1 Answer
May 30, 2016

Answer:

#(7sqrt(3)+13)/22#

Explanation:

Given,

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

Multiply the numerator and denominator by the conjugate of the denominator.

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

Simplify.

#=(10+2sqrt(3)+5sqrt(3)+3)/(25-3)#

#=color(green)(|bar(ul(color(white)(a/a)color(black)((7sqrt(3)+13)/22)color(white)(a/a)|)))#