Question 145229
{{{(2+sqrt(3))^2}}} Start with the given expression



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



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



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



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



{{{4+2*sqrt(3)+2*sqrt(3)+3}}} Now collect every term to make a single expression




{{{7+4*sqrt(3)}}} Now combine like terms



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Answer:

So {{{(2+sqrt(3))^2}}} foils and simplifies to  {{{7+4*sqrt(3)}}}


In other words, {{{(2+sqrt(3))^2=7+4*sqrt(3)}}}