Question 178941
{{{(sqrt(3)-sqrt(5))(sqrt(3)-sqrt(5))}}} Start with the given expression



Let {{{a=sqrt(3)}}} and {{{b=sqrt(5)}}}



{{{(a-b)(a-b)}}} Replace each {{{sqrt(3)}}} with "a" and each {{{sqrt(5)}}} with "b"



{{{a^2-ab-ab+b^2}}} FOIL



{{{a^2-2ab+b^2}}} Combine like terms.



{{{a^2-2ab+b^2}}} Combine like terms.



{{{(sqrt(3))^2-2*sqrt(3)*sqrt(5)+(sqrt(5))^2}}} Plug in {{{a=sqrt(3)}}} and {{{b=sqrt(5)}}}



{{{(sqrt(3))^2-2*sqrt(15)+(sqrt(5))^2}}} Multiply and combine the radicals



{{{3-2*sqrt(15)+5}}} Square {{{sqrt(3)}}} to get 3 and square {{{sqrt(5)}}} to get 5



{{{8-2*sqrt(15)}}} Combine like terms.



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Answer:



So {{{(sqrt(3)-sqrt(5))(sqrt(3)-sqrt(5))=8-2*sqrt(15)}}}