How do you combine #\sqrt { 27} + 3\sqrt { 12} - 9\sqrt { 8}#?

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Answer 1 · 2017-09-02T20:47:15

#9(sqrt(3)-2sqrt(2))#

With roots, the best way to approach the simplification is to look for factors that are squares. Let's look at #sqrt(27)#

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

9 has a square root, so we can pull its root out from under the radical.

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

So now let's simplify the other roots the same way:

#3sqrt(3)+3sqrt(4*3)-9sqrt(4*2)#

#3sqrt(3)+(3*2)sqrt(3)-(9*2)sqrt(2)#

#3sqrt(3)+6sqrt(3)-18sqrt(2)#

We can combine the two #sqrt(3)# terms.

#9sqrt(3)-18sqrt(2)#

Last, if you want, you can pull the common factor of 9 out:

#9(sqrt(3)-2sqrt(2))#