SOLUTION: please help to simplify : 3 times the square root of 3/7 - 2 times the square root of 7/3

SOLUTION: please help to simplify : 3 times the square root of 3/7 - 2 times the square root of 7/3 - the square root of 189 thank you

Question 64835This question is from textbook An Incremental Development
: please help to simplify :
3 times the square root of 3/7 - 2 times the square root of 7/3 - the square root of 189
thank you This question is from textbook An Incremental Development

Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
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

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