Question 152340

{{{3*sqrt(3)+2*sqrt(27)-sqrt(12)}}} Start with the given expression




{{{3*sqrt(3)+2*3*sqrt(3)-sqrt(12)}}} Simplify {{{sqrt(27)}}} to get {{{3*sqrt(3)}}}. 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*sqrt(3)+2*3*sqrt(3)-2*sqrt(3)}}} Simplify {{{sqrt(12)}}} to get {{{2*sqrt(3)}}}.



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

 

Since we have the common term {{{sqrt(3)}}}, we can combine like terms



{{{(3+6-2)sqrt(3)}}} Combine like terms. Remember, {{{5x+3x-4x=(5+3-4)x=4x}}}



{{{7*sqrt(3)}}} Now simplify {{{3+6-2}}} to get {{{7}}}



So {{{3*sqrt(3)+2*sqrt(27)-sqrt(12)}}} simplifies to {{{7*sqrt(3)}}}. 



In other words,  {{{3*sqrt(3)+2*sqrt(27)-sqrt(12)=7*sqrt(3)}}}