SOLUTION: Dear tutors, Please explain how to solve : 1/(2

SOLUTION: Dear tutors, Please explain how to solve : 1/(2 - sqrt(3))? Thanks for your help.

Question 5724: Dear tutors,
Please explain how to solve : 1/(2 - sqrt(3))?
Thanks for your help.
Answer by guapa(62) (Show Source): You can put this solution on YOUR website!
You are supposed to evaluate this radical expression. To express it in simplest radical form you have to get rid of the radical in the denominator. You do that by rationalizing the denominator (multiply the fraction by a form of 1).In your example you have a binominal term in the denominator. (2-sqrt3) That means in this case we use its conjugate which is 2+sqrt3 {(2+sqrt3)/(2+sqrt3) is merely a form of 1}.
{1*(2+sqrt3)}/{(2-sqrt3)*(2+sqrt3)} Now let's simplify the fraction.
(2+sqrt3)/(4-sqrt9) Since 9 is a perfect square we get
(2+sqrt3)/(4-3) = (2+sqrt3)/1 That results into
2+sqrt3 which is your final answer.
I hope that helps

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