Question 190596
{{{-3*sqrt(24)+2*sqrt(54)-sqrt(6)}}} Start with the given expression



{{{-3*2*sqrt(6)+2*sqrt(54)-sqrt(6)}}} Simplify {{{sqrt(24)}}} to get {{{2*sqrt(6)}}}. Note: If you need help with simplifying square roots, check out this <a href=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>.



{{{-3*2*sqrt(6)+2*3*sqrt(6)-sqrt(6)}}} Simplify {{{sqrt(54)}}} to get {{{3*sqrt(6)}}}.



{{{-6*sqrt(6)+2*3*sqrt(6)-sqrt(6)}}} Multiply 3 and 2 to get 6.

 


{{{-6*sqrt(6)+6*sqrt(6)-sqrt(6)}}} Multiply 2 and 3 to get 6.

 

Since we have the common term {{{sqrt(6)}}}, we can combine like terms


{{{(-6+6-1)sqrt(6)}}} Combine like terms. Remember, {{{5x+3x-4x=(5+3-4)x=4x}}}



{{{-sqrt(6)}}} Now simplify {{{-6+6-1}}} to get {{{-1}}}



So {{{-3*sqrt(24)+2*sqrt(54)-sqrt(6)}}} simplifies to {{{-sqrt(6)}}}. 



In other words,  {{{-3*sqrt(24)+2*sqrt(54)-sqrt(6)=-sqrt(6)}}}