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

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Answer 1 · 2014-11-05T18:30:01

#sqrt{2}-sqrt{27}+2sqrt{54}+3sqrt{48}#

by #27=3^3#, #54=2 cdot 3^3#, and #48=2^4 cdot 3#,

#=sqrt{6}-sqrt{3^3}+2sqrt{2 cdot 3^3}+3sqrt{2^4 cdot 3}#

by pulling out factors out of the square-roots,

#=sqrt{6}-3sqrt{3}+6sqrt{6}+12sqrt{3}#

by combining the like terms,

#=7sqrt{6}+9sqrt{3}#

I hope that this was helpful.