document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=469802>Question 469802</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do I add or subtract irrational numbers?<BR>\n" );
document.write( "e.g <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+19sqrt%282%29-6sqrt%282%29+ ALIGN=MIDDLE  ALT=\"+19sqrt%282%29-6sqrt%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I have been told it is the same as rational numbers but do not understand this </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #322278 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=322278\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For your particular problem, it is possible to subtract these two terms because the quantity under the square root sign is the same for both terms.<BR>\n" );
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document.write( "For this problem, you can think of it this way:<BR>\n" );
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document.write( "You were given:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=19%2Asqrt%282%29-6%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"19%2Asqrt%282%29-6%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%29 ALIGN=MIDDLE  ALT=\"sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is common to both terms, you can factor it out.  In factored form your problem becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2819+-+6%29%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"%2819+-+6%29%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now combine the two numbers inside the parentheses, that is subtract 6 from 19 and you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"13%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and this is the answer to the subtraction problem that you started with. <BR>\n" );
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document.write( "Remember, this method of combining (adding or subtracting) is only possible if the irrational terms are the same.  If your original problem had been:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=19%2Asqrt%282%29+-+6%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"19%2Asqrt%282%29+-+6%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "then you could not combine the two terms using addition or subtraction. You can recognize this by the fact that you cannot factor out the irrational radicals because they are different in each of the two terms.<BR>\n" );
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document.write( "Hope this helps you understand the addition and subtraction process for irrational numbers a little better. Once you get used to ensuring that terms in the radicals are the same, you will just be able to say \"19 times the square root of two minus 6 times the square root of 2 is 13 times the square root of two without wasting time by going through the factoring process. I just showed you the factoring in hopes that it would help you understand what is going on in the problem a little better. Good luck. \r<BR>\n" );
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