Question 264527
Some scratch work: 


{{{sqrt(48)=sqrt(16*3)=sqrt(16)*sqrt(3)=4*sqrt(3)}}}. So {{{sqrt(48)=4*sqrt(3)}}}



{{{sqrt(27)=sqrt(9*3)=sqrt(9)*sqrt(3)=3*sqrt(3)}}}. So {{{sqrt(27)=3*sqrt(3)}}} 



{{{sqrt(54)=sqrt(9*6)=sqrt(9)*sqrt(6)=3*sqrt(6)}}}. So {{{sqrt(54)=3*sqrt(6)}}}


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{{{5*sqrt(48)-sqrt(27)+3*sqrt(54)}}} Start with the given expression.



{{{5*4*sqrt(3)-3*sqrt(3)+3*3*sqrt(6)}}} Simplify the radicals (see scratch work above).



{{{20*sqrt(3)-3*sqrt(3)+9*sqrt(6)}}} Multiply



{{{17*sqrt(3)+9*sqrt(6)}}} Combine like terms.



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Answer:



So 
{{{5*sqrt(48)-sqrt(27)+3*sqrt(54)=17*sqrt(3)+9*sqrt(6)}}}