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

1 Answer
Nov 5, 2014

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.