Question 119046
I'll do the first three to help you get started.



#1


{{{7*sqrt(72)-2*sqrt(50)}}} Start with the given expression



{{{7*6*sqrt(2)-2*sqrt(50)}}} Simplify {{{sqrt(72)}}} to get {{{6*sqrt(2)}}}. 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>.



{{{7*6*sqrt(2)-2*5*sqrt(2)}}} Simplify {{{sqrt(50)}}} to get {{{5*sqrt(2)}}}.



{{{42*sqrt(2)-2*5*sqrt(2)}}} Multiply 7 and 6 to get 42.

 

{{{42*sqrt(2)-10*sqrt(2)}}} Multiply 2 and 5 to get 10.

 

Since we have the common term {{{sqrt(2)}}}, we can combine like terms


{{{(42-10)sqrt(2)}}} Combine like terms. Remember, {{{5x+3x-4x=(5+3-4)x=4x}}}



{{{32*sqrt(2)}}} Now simplify {{{42-10}}} to get {{{32}}}


So {{{7*sqrt(72)-2*sqrt(50)}}} simplifies to {{{32*sqrt(2)}}}. In other words,  {{{7*sqrt(72)-2*sqrt(50)=32*sqrt(2)}}}




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{{{ 2^3sqrt(54x^4) - 3^3sqrt(16x^4)}}} Start with the given expression




{{{ 8*sqrt(54x^4) - 27*sqrt(16x^4)}}} Evaluate {{{2^3}}} to get 8. Evaluate {{{3^3}}} to get 27




{{{ 8*sqrt(9*6*x^2*x^2) - 27*sqrt(4*4*x^2*x^2)}}} Factor {{{54x^4}}} into {{{9*6*x^2*x^2}}}. Factor {{{16x^4}}} into {{{4*4*x^2*x^2}}}





{{{ 8*sqrt(9)*sqrt(6)*sqrt(x^2)*sqrt(x^2) - 27*sqrt(16)*sqrt(x^2)*sqrt(x^2)}}} Break up the square roots




{{{ 8*3*sqrt(6)*x*x - 27*4*x*x}}} Take the square root.




{{{ 24x^2*sqrt(6) - 108x^2}}} Multiply




So {{{ 2^3sqrt(54x^4) - 3^3sqrt(16x^4)}}} simplifies to {{{24x^2*sqrt(6) - 108x^2}}}. 


In other words, {{{ 2^3sqrt(54x^4) - 3^3sqrt(16x^4)=24x^2*sqrt(6) - 108x^2}}}




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#3





{{{6*sqrt(98)-9*sqrt(32)-3*sqrt(200)}}} Start with the given expression



{{{6*7*sqrt(2)-9*sqrt(32)-3*sqrt(200)}}} Simplify {{{sqrt(98)}}} to get {{{7*sqrt(2)}}}. 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>.



{{{6*7*sqrt(2)-9*4*sqrt(2)-3*sqrt(200)}}} Simplify {{{sqrt(32)}}} to get {{{4*sqrt(2)}}}.



{{{6*7*sqrt(2)-9*4*sqrt(2)-3*10*sqrt(2)}}} Simplify {{{sqrt(200)}}} to get {{{10*sqrt(2)}}}.



{{{42*sqrt(2)-9*4*sqrt(2)-3*10*sqrt(2)}}} Multiply 6 and 7 to get 42.

 

{{{42*sqrt(2)-36*sqrt(2)-3*10*sqrt(2)}}} Multiply 9 and 4 to get 36.

 

{{{42*sqrt(2)-36*sqrt(2)-30*sqrt(2)}}} Multiply 3 and 10 to get 30.

 

Since we have the common term {{{sqrt(2)}}}, we can combine like terms


{{{(42-36-30)sqrt(2)}}} Combine like terms. Remember, {{{5x+3x-4x=(5+3-4)x=4x}}}



{{{-24*sqrt(2)}}} Now simplify {{{42-36-30}}} to get {{{-24}}}


So {{{6*sqrt(98)-9*sqrt(32)-3*sqrt(200)}}} simplifies to {{{-24*sqrt(2)}}}. In other words,  {{{6*sqrt(98)-9*sqrt(32)-3*sqrt(200)=-24*sqrt(2)}}}