How do you simplify (sqrt2-sqrt3)/(sqrt2+sqrt3)?

1 Answer
smendyka
Nov 6, 2017

See a solution process below:

Explanation:

To eliminate the radicals from the denominator (or to rationalize the denominator) we can multiply the fraction by the appropriate form of 1. In this case;

(sqrt(2) - sqrt(3))/(sqrt(2) - sqrt(3))

(sqrt(2) - sqrt(3))/(sqrt(2) - sqrt(3)) xx (sqrt(2) - sqrt(3))/(sqrt(2) + sqrt(3)) =>

((sqrt(2))^2 - sqrt(2)sqrt(3) - sqrt(3)sqrt(2) + (sqrt(3))^2)/((sqrt(2))^2 + sqrt(2)sqrt(3) - sqrt(3)sqrt(2) - (sqrt(3))^2) =>

(2 - sqrt(6) - sqrt(6) + 3)/(2 + 0 - 3) =>

(5 - 2sqrt(6))/(-1) =>

-5 + 2sqrt(6)

Or

2sqrt(6) - 5

Related questions
See all questions in Multiplication and Division of Radicals
Impact of this question
2872 views around the world
You can reuse this answer
Creative Commons License