Question 169974


{{{(sqrt(3)+sqrt(2))^2}}} Start with the given expression.



{{{(sqrt(3)+sqrt(2))(sqrt(3)+sqrt(2))}}} Expand. Remember something like {{{x^2=x*x}}}.



Now let's FOIL the expression.



Remember, when you FOIL an expression, you follow this procedure:



{{{(highlight(sqrt(3))+sqrt(2))(highlight(sqrt(3))+sqrt(2))}}} Multiply the <font color="red">F</font>irst terms:{{{(sqrt(3))*(sqrt(3))=sqrt(9)=3}}}.



{{{(highlight(sqrt(3))+sqrt(2))(sqrt(3)+highlight(sqrt(2)))}}} Multiply the <font color="red">O</font>uter terms:{{{(sqrt(3))*(sqrt(2))=sqrt(6)}}}.



{{{(sqrt(3)+highlight(sqrt(2)))(highlight(sqrt(3))+sqrt(2))}}} Multiply the <font color="red">I</font>nner terms:{{{(sqrt(2))*(sqrt(3))=sqrt(6)}}}.



{{{(sqrt(3)+highlight(sqrt(2)))(sqrt(3)+highlight(sqrt(2)))}}} Multiply the <font color="red">L</font>ast terms:{{{(sqrt(2))*(sqrt(2))=sqrt(4)=2}}}.



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{{{3+sqrt(6)+sqrt(6)+2}}} Now collect every term to make a single expression.



{{{5+2*sqrt(6)}}} Now combine like terms.



So {{{(sqrt(3)+sqrt(2))^2}}} FOILs to {{{5+2*sqrt(6)}}}.



In other words, {{{(sqrt(3)+sqrt(2))^2=5+2*sqrt(6)}}}.