How do you combine the radical \sqrt{6}-\sqrt{27}+2\sqrt{54}+3\sqrt{48}627+254+348?

1 Answer
Nov 5, 2014

sqrt{2}-sqrt{27}+2sqrt{54}+3sqrt{48}227+254+348

by 27=3^327=33, 54=2 cdot 3^354=233, and 48=2^4 cdot 348=243,

=sqrt{6}-sqrt{3^3}+2sqrt{2 cdot 3^3}+3sqrt{2^4 cdot 3}=633+2233+3243

by pulling out factors out of the square-roots,

=sqrt{6}-3sqrt{3}+6sqrt{6}+12sqrt{3}=633+66+123

by combining the like terms,

=7sqrt{6}+9sqrt{3}=76+93


I hope that this was helpful.