Question 64835
To Simplify:

3sqrt(3/7)-2sqrt(7/3)-sqrt(189) First, lets rewrite sqrt (189)
sqrt(189)=sqrt((9)(21))=
3sqrt(21)

so we now have:

3sqrt(3/7)-2sqrt(7/3)-3sqrt(21)  

Looks like the lowest common multiple (LCM) for 3 and 7 is 21. (LCM is the smallest number that both 3 and 7 divides evenly into.)

Now we will multiply every term by sqrt(21/21).  This will eventually give us a common denominator.

(3sqrt(3/7))(sqrt(21/21))-(2sqrt(7/3))(sqrt(21/21))-3sqrt(21)(sqrt(21/21)) simplifying, we get:

((3)(3))/sqrt(21)-((2)(7))/sqrt(21)-((3)(21))/sqrt(21) simplifying further:


(9-14-63)/sqrt(21)=
-68/sqrt(21) once more, we will multiply by the sqrt(21/21)) and we get:

(-68sqrt(21))/21

You can check this answer using a calculator.

Hope this helps.  Happy holidays-----ptaylor