document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=62071>Question 62071</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I'm having a hard enough time in Algebra - now they want me to deal with \"imaginary\" numbers?  I'm having trouble with simplifying (using i):\r<BR>\n" );
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document.write( "sqrt(-8) + sqrt(-50)\r<BR>\n" );
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document.write( "can someone help, please? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #42835 by </B><A HREF=/tutors/aboutme.mpl?userid=ptaylor><B>ptaylor(2198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ptaylor><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=ptaylor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=42835\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  I'll Try.\r<BR>\n" );
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document.write( "You know that the sqrt of a number is another number that, when multiplied by itself, yields the original number.  For example, the sqrt of 9 is plus 3 or minus 3 since minus times minus equals a plus.  Now, lets look at the sqrt <BR>\n" );
document.write( "of -9.  Clearly, there are no real numbers that can be multiplied by themselves to yield a -9. Thus, the definition \"sqrt(-1)=i\" and i is defined as an imaginary number. \r<BR>\n" );
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document.write( "Now we also know that the sqrt (-8) is equal to the sqrt (-1) times sqrt(8) which also equals sqrt(-1) times sqrt (4) times sqrt(2). simplifying:<BR>\n" );
document.write( "sqrt (-1)=i<BR>\n" );
document.write( "sqrt (4)=2<BR>\n" );
document.write( "sqrt2=sqrt2\r<BR>\n" );
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document.write( "we now have:<BR>\n" );
document.write( "sqrt(-8)=(2i)(sqrt (2)) \r<BR>\n" );
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document.write( "Likewise sqrt (-50) equals sqrt (-1) times sqrt (50) which also equals     sqrt (-1) times sqrt (2) times sqrt (25). simplifying, we have<BR>\n" );
document.write( "sqrt (-1)=i<BR>\n" );
document.write( "sqrt (25)=5<BR>\n" );
document.write( "sqrt (2)=sqrt (2)\r<BR>\n" );
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document.write( "We now have:<BR>\n" );
document.write( "sqrt(-50)=(5i)(sqrt(2)) Finally:\r<BR>\n" );
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document.write( "sqrt(-8)+sqrt(-50)= (2i)(sqrt(2))+(5i)(sqrt(2)) which equals<BR>\n" );
document.write( "(sqrt(2))(5i+2i)=(7i)(sqrt(2))\r<BR>\n" );
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document.write( "Hope this helps. I know it does get confusing sometimes ----ptaylor\r<BR>\n" );
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document.write( "  </SPAN>\n" );
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