|1-sqrt(3)|+|2-sqrt(3)|=1 WHY? :/

$${\sqrt{{\mathtt{3}}}} = {\mathtt{1.732\: \!050\: \!807\: \!568\: \!877\: \!3}}$$

$${\left|{\mathtt{1}}{\mathtt{\,-\,}}{\sqrt{{\mathtt{3}}}}\right|} = {\mathtt{0.732\: \!050\: \!807\: \!568\: \!877\: \!3}}$$

$${\left|{\mathtt{2}}{\mathtt{\,-\,}}{\sqrt{{\mathtt{3}}}}\right|} = {\mathtt{0.267\: \!949\: \!192\: \!431\: \!122\: \!7}}$$

Add up the last two (which are only approximate, as √3 is irrational) to get 1.

Or:  |1 - √3| = √3 - 1 because √3 is bigger than 1

       |2 - √3| = 2 - √3 because 2 is bigger than √3

Add these up and the √3's cancel out, leaving 2 - 1 = 1.