document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=884962>Question 884962</A>: <I><SPAN STYLE=\"word-break: break-all;\"> why square root of -2 is not a real number and what we have to see a number is real or not  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #534817 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39618)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=534817\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> sqrt(-2) is imaginary.  REAL numbers have REAL solutions for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-n=0 ALIGN=MIDDLE  ALT=\"x%5E2-n=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%3E0 ALIGN=MIDDLE  ALT=\"n%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  n does not need to be a perfect square.  n just needs to be positive or equal to zero.  \r<BR>\n" );
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document.write( "You know <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-4=0 ALIGN=MIDDLE  ALT=\"x%5E2-4=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be solved to find x=2 or x=-2.  How?  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=4 ALIGN=MIDDLE  ALT=\"x%5E2=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%5E2%29=sqrt%284%29=0%2B-+2 ALIGN=MIDDLE  ALT=\"sqrt%28x%5E2%29=sqrt%284%29=0%2B-+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "You know <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-25=0 ALIGN=MIDDLE  ALT=\"x%5E2-25=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be solved to find x=5 or x=-5.\r<BR>\n" );
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document.write( "Try <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B1=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B1-1=0-1 ALIGN=MIDDLE  ALT=\"x%5E2%2B1-1=0-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=-1 ALIGN=MIDDLE  ALT=\"x%5E2=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%5E2%29=0%2B-+sqrt%28-1%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%5E2%29=0%2B-+sqrt%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >;  What is that?  \r<BR>\n" );
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document.write( "Square root of a positive number we can make sense.  Square root of a negative number is different.  One way to deal with this was to invent a different kind of number.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i%5E2=-1 ALIGN=MIDDLE  ALT=\"i%5E2=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > uses the imaginary number, i, according to this shown equation.  Now with that simple-looking equation, the square root can be found as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28i%5E2%29=i=0%2B-+sqrt%28-1%29 ALIGN=MIDDLE  ALT=\"sqrt%28i%5E2%29=i=0%2B-+sqrt%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The number, i, is often used as the imaginary unit to help in writing imaginary numbers.\r<BR>\n" );
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document.write( "(I have included the 0 in a couple of the equations only to help with rendering.  Usually, that addition or subtraction of zero is unnecessary).\r<BR>\n" );
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document.write( "Square Root of -2<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28-2%29=sqrt%28-1%2A2%29=sqrt%28-1%29sqrt%282%29=i%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"sqrt%28-2%29=sqrt%28-1%2A2%29=sqrt%28-1%29sqrt%282%29=i%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which is an imaginary number. </SPAN>\n" );
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