Expert: Sherman D. - 6/23/2004

Question
How do you simplify the expression:


  2 - (sqrt)3
 ---------------        
  2 + (sqrt)3   


2 minus the square root of 3 all over 2 plus the square root of 3.  

I am not sure if you can cancel anything our or not.  I am not sure where to begin on this problem.

Answer
(2 - sqrt(3))/(2 + sqrt(3))

Multiply top and bottom by (2 - sqrt(3))

(((2 - sqrt(3)) * (2 - sqrt(3)))/(((2 + sqrt(3)) * (2 - sqrt(3)))

This gives you

(4 - 2sqrt(3) - 2sqrt(3) + (sqrt(3))^2)/((4 - 2sqrt(3) + 2sqrt(3) - (sqrt(3))^2)

This gives you

(4 + (-2 - 2)sqrt(3) + 3)/(4 + (-2 + 2)sqrt(3) - 3)

(4 + (-2 + (-2))sqrt(3) + 3)/(4 + (-2 - (-2))sqrt(3) - 3)

(4 - 4sqrt(3) + 3)/(4 - 3)

((4 + 3) - 4sqrt(3))/1

7 - 4sqrt(3)

thats

7 minus 4*sqrt(3)

and in case you don't know * means to multiply.