document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=498435>Question 498435</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I was wondering how to simplify the equation (-5-sqrt-3)^2\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #337041 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=337041\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if i understand your equation, it is (-5-sqrt(-3))^2\r<BR>\n" );
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document.write( "(-5-sqrt(-3))^2 is equal to:<BR>\n" );
document.write( "(-5-sqrt(-3)) * (-5-sqrt(-3)) which is equal to:<BR>\n" );
document.write( "-5*(-5-sqrt(-3)) - sqrt(-3)*(-5-sqrt(-3))<BR>\n" );
document.write( "this is because of the distributive property of algebra operations that states:<BR>\n" );
document.write( "(a + b) * (c + d) is equal to a*(c + d) + b*(c + d)<BR>\n" );
document.write( "multiplying out those terms gets:<BR>\n" );
document.write( "25 + 5*sqrt(-3) + 5*sqrt(-3) + sqrt(-3)*sqrt(-3)<BR>\n" );
document.write( "combine like terms and you get:<BR>\n" );
document.write( "25 + 10*sqrt(-3) + (sqrt(-3))^2 <BR>\n" );
document.write( "simplify this further to get:<BR>\n" );
document.write( "25 + 10*sqrt(-3) - 3<BR>\n" );
document.write( "simplify this further to get:<BR>\n" );
document.write( "22 + 10*sqrt(-3)\r<BR>\n" );
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document.write( "note that 22 + sqrt(-3) does not provide you with a real number.<BR>\n" );
document.write( "the answer of 22 + 10*sqrt(-3) is a complex number.<BR>\n" );
document.write( "it has a real part (22) and it has an imaginary part (10*sqrt(-3)).<BR>\n" );
document.write( "never the less, (sqrt(-3))^2 does get you an answer of -3.<BR>\n" );
document.write( "this is because when  you square the square of a number, you get the number.<BR>\n" );
document.write( "example:<BR>\n" );
document.write( "(sqrt(4))^2 = 4 (sqrt(4) = 2 and 2^2 = 4)\r<BR>\n" );
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document.write( "back to your complex number....<BR>\n" );
document.write( "22 + 10*sqrt(-3) is a complex number.<BR>\n" );
document.write( "it can be simplified further as follows:<BR>\n" );
document.write( "sqrt(-3) = sqrt(3)*i, where i is equal to sqrt(-1)<BR>\n" );
document.write( "your answer can therefore be shown as:<BR>\n" );
document.write( "22 + 10*sqrt(3)*i\r<BR>\n" );
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