Question 199837
{{{13*sqrt(20)-15*sqrt(32)-8*sqrt(45)+7*sqrt(8)}}} Start with the given expression



{{{13*2*sqrt(5)-15*sqrt(32)-8*sqrt(45)+7*sqrt(8)}}} Simplify {{{sqrt(20)}}} to get {{{2*sqrt(5)}}}. 



{{{13*2*sqrt(5)-15*4*sqrt(2)-8*sqrt(45)+7*sqrt(8)}}} Simplify {{{sqrt(32)}}} to get {{{4*sqrt(2)}}}.



{{{13*2*sqrt(5)-15*4*sqrt(2)-8*3*sqrt(5)+7*sqrt(8)}}} Simplify {{{sqrt(45)}}} to get {{{3*sqrt(5)}}}.



{{{13*2*sqrt(5)-15*4*sqrt(2)-8*3*sqrt(5)+7*2*sqrt(2)}}} Simplify {{{sqrt(8)}}} to get {{{2*sqrt(2)}}}.



{{{26*sqrt(5)-15*4*sqrt(2)-8*3*sqrt(5)+7*2*sqrt(2)}}} Multiply 13 and 2 to get 26.


 

{{{26*sqrt(5)-60*sqrt(2)-8*3*sqrt(5)+7*2*sqrt(2)}}} Multiply 15 and 4 to get 60.

 


{{{26*sqrt(5)-60*sqrt(2)-24*sqrt(5)+7*2*sqrt(2)}}} Multiply 8 and 3 to get 24.

 


{{{26*sqrt(5)-60*sqrt(2)-24*sqrt(5)+14*sqrt(2)}}} Multiply 7 and 2 to get 14.

 
 

{{{2*sqrt(5)-46*sqrt(2)}}} Combine like terms.




So {{{13*sqrt(20)-15*sqrt(32)-8*sqrt(45)+7*sqrt(8)}}} simplifies to {{{2*sqrt(5)-46*sqrt(2)}}}. 




In other words,  {{{13*sqrt(20)-15*sqrt(32)-8*sqrt(45)+7*sqrt(8)=2*sqrt(5)-46*sqrt(2)}}}