How do you rationalize the denominator and simplify (2+ sqrt 3)/(5- sqrt 3)2+√35−√3?

1 Answer
Johnson Z.
May 30, 2016

(7sqrt(3)+13)/227√3+1322

Explanation:

Given,

(2+sqrt(3))/(5-sqrt(3))2+√35−√3

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

=(2+sqrt(3))/(5-sqrt(3))*((5+sqrt(3))/(5+sqrt(3)))=2+√35−√3⋅(5+√35+√3)

Simplify.

=(10+2sqrt(3)+5sqrt(3)+3)/(25-3)=10+2√3+5√3+325−3

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

Related questions
See all questions in Multiplication and Division of Radicals
Impact of this question
2716 views around the world
You can reuse this answer
Creative Commons License