Question 171553


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



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



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



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



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



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{{{9+3*sqrt(2)+3*sqrt(2)+2}}} Now collect every term to make a single expression.



{{{11+6*sqrt(2)}}} Now combine like terms.



So {{{(3+sqrt(2))^2}}} FOILs to {{{11+6*sqrt(2)}}}.



In other words, {{{(3+sqrt(2))^2=11+6*sqrt(2)}}}.