# The coordinates of A and B are 27 square root and 15 square root respectively. Find AB.

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Expert Answers

embizze | Certified Educator

Find AB if the coordinate of A is `sqrt(27)` and the coordinate of B is `sqrt(15)` :

The distance d between two points on a number line a,b is `d=|a-b|` .

So `AB=|sqrt(27)-sqrt(15)|` . Since `sqrt(27)>sqrt(15)` we can drop the absolute value bars.

Then `AB=sqrt(27)-sqrt(15)` . This can be simplified:

`sqrt(27)=sqrt(9*3)=sqrt(9)sqrt(3)=3sqrt(3)`

`sqrt(15)=sqrt(5*3)=sqrt(5)sqrt(3)`

`AB=sqrt(27)-sqrt(15)=3sqrt(3)-sqrt(5)sqrt(3)`

`=sqrt(3)(3-sqrt(5))`

`~~1.323`