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

1 Answer
May 30, 2016

(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)|)))