Question 143279
{{{8*sqrt(5)+9*sqrt(25)+11*sqrt(20)}}} Start with the given expression



{{{8*sqrt(5)+9*5+11*sqrt(20)}}} Simplify {{{sqrt(25)}}} to get {{{5}}}.



{{{8*sqrt(5)+9*5+11*2*sqrt(5)}}} Simplify {{{sqrt(20)}}} to get {{{2*sqrt(5)}}}. 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>.



{{{8*sqrt(5)+45+11*2*sqrt(5)}}} Multiply 9 and 5 to get 45.

 


{{{8*sqrt(5)+45+22*sqrt(5)}}} Multiply 11 and 2 to get 22.



{{{(8*sqrt(5)+22*sqrt(5))+45}}} Group like terms



{{{sqrt(5)(8+22)+45}}} Factor out {{{sqrt(5)}}} from the first group



{{{sqrt(5)(30)+45}}} Combine like terms



{{{45+30*sqrt(5)}}} Rearrange the terms


 
So {{{8*sqrt(5)+9*sqrt(25)+11*sqrt(20)}}} simplifies to {{{45+30*sqrt(5)}}}. In other words,  {{{8*sqrt(5)+9*sqrt(25)+11*sqrt(20)=45+30*sqrt(5)}}}