document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=95958>Question 95958</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have been trying to do this problem for a while now, i tried doing it step by step and also checking it on the calculator but it gives me a different answer every time.\r<BR>\n" );
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document.write( "3square root of 45 -2square root of 125\r<BR>\n" );
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document.write( "this is al together like side by side </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #69895 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=69895\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given to simplify:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Asqrt%2845%29-2%2Asqrt%28125%29 ALIGN=MIDDLE  ALT=\"3%2Asqrt%2845%29-2%2Asqrt%28125%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "On a calculator you can find that the square root of 45 is 6.708203932 so multiplying <BR>\n" );
document.write( "the square root of 45 times 3 results in 3*6.708203932 = 20.1246118. Substituting this number<BR>\n" );
document.write( "into the problem in place of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Asqrt%2845%29 ALIGN=MIDDLE  ALT=\"3%2Asqrt%2845%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > reduces the problem to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20.1246118+-+2%2Asqrt%28125%29 ALIGN=MIDDLE  ALT=\"20.1246118+-+2%2Asqrt%28125%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Next you can use the calculator to find that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28125%29+=+11.18033989 ALIGN=MIDDLE  ALT=\"sqrt%28125%29+=+11.18033989\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Multiplying this<BR>\n" );
document.write( "by -2 results in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2Asqrt%28125%29+=+-2%2A11.18033989+=+-22.36067977 ALIGN=MIDDLE  ALT=\"-2%2Asqrt%28125%29+=+-2%2A11.18033989+=+-22.36067977\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Then substituting this <BR>\n" );
document.write( "into the equation reduces the equation to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20.1246118+-+22.36067977+=+-2.236067975 ALIGN=MIDDLE  ALT=\"20.1246118+-+22.36067977+=+-2.236067975\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So the answer to this problem is -2.236067975 within the roundoff error on the last decimal <BR>\n" );
document.write( "place.<BR>\n" );
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document.write( "Now let's work the problem without doing it on a calculator. Start with:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Asqrt%2845%29-2%2Asqrt%28125%29 ALIGN=MIDDLE  ALT=\"3%2Asqrt%2845%29-2%2Asqrt%28125%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Note that by the rules of radicals, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2845%29+=+sqrt%289%2A5%29+=+sqrt%289%29%2Asqrt%285%29+=+3%2Asqrt%285%29 ALIGN=MIDDLE  ALT=\"sqrt%2845%29+=+sqrt%289%2A5%29+=+sqrt%289%29%2Asqrt%285%29+=+3%2Asqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So you can substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Asqrt%285%29 ALIGN=MIDDLE  ALT=\"3%2Asqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2845%29 ALIGN=MIDDLE  ALT=\"sqrt%2845%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A3%2Asqrt%285%29+-+2%2Asqrt%28125%29 ALIGN=MIDDLE  ALT=\"3%2A3%2Asqrt%285%29+-+2%2Asqrt%28125%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now let's simplify <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28125%29 ALIGN=MIDDLE  ALT=\"sqrt%28125%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28125%29+=+sqrt%2825%2A5%29+=+sqrt%2825%29%2Asqrt%285%29=+5%2Asqrt%285%29 ALIGN=MIDDLE  ALT=\"sqrt%28125%29+=+sqrt%2825%2A5%29+=+sqrt%2825%29%2Asqrt%285%29=+5%2Asqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You can now substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2Asqrt%285%29 ALIGN=MIDDLE  ALT=\"5%2Asqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28125%29 ALIGN=MIDDLE  ALT=\"sqrt%28125%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A3%2Asqrt%285%29+-+2%2A5%2Asqrt%285%29 ALIGN=MIDDLE  ALT=\"3%2A3%2Asqrt%285%29+-+2%2A5%2Asqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Do the multiplications. 3*3 = 9 and -2*5 = -10. So this becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2Asqrt%285%29+-+10%2Asqrt%285%29 ALIGN=MIDDLE  ALT=\"9%2Asqrt%285%29+-+10%2Asqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You can factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%285%29 ALIGN=MIDDLE  ALT=\"sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > from each term to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289-10%29%2Asqrt%285%29 ALIGN=MIDDLE  ALT=\"%289-10%29%2Asqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Combine the two numbers in the parentheses to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%29%2Asqrt%285%29+=+-1%2Asqrt%285%29+=+-sqrt%285%29 ALIGN=MIDDLE  ALT=\"%28-1%29%2Asqrt%285%29+=+-1%2Asqrt%285%29+=+-sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So the answer we got is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-sqrt%285%29 ALIGN=MIDDLE  ALT=\"-sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. If you find the square root of 5 on a calculator<BR>\n" );
document.write( "you will find that it is 2.236067977. Therefore, our answer becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-sqrt%285%29+=+-2.236067977 ALIGN=MIDDLE  ALT=\"-sqrt%285%29+=+-2.236067977\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This agrees with the answer we got by doing all the work on a calculator. So you can use<BR>\n" );
document.write( "either method depending on what is compatible with the way your teacher wants it done.<BR>\n" );
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document.write( "Hope this helps you to understand the problem and how to get the answer.<BR>\n" );
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