document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1192821>Question 1192821</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Simplify Completely, keep all answers and work in radical form<BR>\n" );
document.write( "5*sqrt(128x^3)+4*sqrt(98x^2)-3x*sqrt(162x) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #824737 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=824737\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Notice that 128 = 64*2 showing that 64 is the largest perfect square factor of 128.<BR>\n" );
document.write( "Similarly, x^2 is the largest perfect square factor of x^3\r<BR>\n" );
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document.write( "We can rewrite 128x^3 into 64x^2*2x to be able to perform this simplification<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28128x%5E3%29+=+sqrt%2864x%5E2%2A2x%29 ALIGN=MIDDLE  ALT=\"sqrt%28128x%5E3%29+=+sqrt%2864x%5E2%2A2x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28128x%5E3%29+=+sqrt%2864x%5E2%29%2Asqrt%282x%29 ALIGN=MIDDLE  ALT=\"sqrt%28128x%5E3%29+=+sqrt%2864x%5E2%29%2Asqrt%282x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use the rule that sqrt(A*B) = sqrt(A)*sqrt(B)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28128x%5E3%29+=+sqrt%28%288x%29%5E2%29%2Asqrt%282x%29 ALIGN=MIDDLE  ALT=\"sqrt%28128x%5E3%29+=+sqrt%28%288x%29%5E2%29%2Asqrt%282x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28128x%5E3%29+=+8x%2Asqrt%282x%29 ALIGN=MIDDLE  ALT=\"sqrt%28128x%5E3%29+=+8x%2Asqrt%282x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Such that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3E=+0 ALIGN=MIDDLE  ALT=\"x+%3E=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Through similar logic, we can also say:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2898x%5E2%29+=+sqrt%2849x%5E2%2A2%29 ALIGN=MIDDLE  ALT=\"sqrt%2898x%5E2%29+=+sqrt%2849x%5E2%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2898x%5E2%29+=+sqrt%2849x%5E2%29%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"sqrt%2898x%5E2%29+=+sqrt%2849x%5E2%29%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2898x%5E2%29+=+sqrt%28%287x%29%5E2%29%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"sqrt%2898x%5E2%29+=+sqrt%28%287x%29%5E2%29%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2898x%5E2%29+=+7x%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"sqrt%2898x%5E2%29+=+7x%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "And also,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28162x%29+=+sqrt%2881%2A2x%29 ALIGN=MIDDLE  ALT=\"sqrt%28162x%29+=+sqrt%2881%2A2x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28162x%29+=+sqrt%2881%29%2Asqrt%282x%29 ALIGN=MIDDLE  ALT=\"sqrt%28162x%29+=+sqrt%2881%29%2Asqrt%282x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28162x%29+=+9%2Asqrt%282x%29 ALIGN=MIDDLE  ALT=\"sqrt%28162x%29+=+9%2Asqrt%282x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Use the three results we got earlier above to simplify the given expresdsion like so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2Asqrt%28128x%5E3%29%2B4%2Asqrt%2898x%5E2%29-3x%2Asqrt%28162x%29 ALIGN=MIDDLE  ALT=\"5%2Asqrt%28128x%5E3%29%2B4%2Asqrt%2898x%5E2%29-3x%2Asqrt%28162x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2A8x%2Asqrt%282x%29%2B4%2A7x%2Asqrt%282%29-3x%2A9%2Asqrt%282x%29 ALIGN=MIDDLE  ALT=\"5%2A8x%2Asqrt%282x%29%2B4%2A7x%2Asqrt%282%29-3x%2A9%2Asqrt%282x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40x%2Asqrt%282x%29%2B28x%2Asqrt%282%29-27x%2Asqrt%282x%29 ALIGN=MIDDLE  ALT=\"40x%2Asqrt%282x%29%2B28x%2Asqrt%282%29-27x%2Asqrt%282x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40x%2Asqrt%282x%29-27x%2Asqrt%282x%29%2B28x%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"40x%2Asqrt%282x%29-27x%2Asqrt%282x%29%2B28x%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2840x-27x%29%2Asqrt%282x%29%2B28x%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"%2840x-27x%29%2Asqrt%282x%29%2B28x%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13x%2Asqrt%282x%29%2B28x%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"13x%2Asqrt%282x%29%2B28x%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Therefore,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2Asqrt%28128x%5E3%29%2B4%2Asqrt%2898x%5E2%29-3x%2Asqrt%28162x%29 ALIGN=MIDDLE  ALT=\"5%2Asqrt%28128x%5E3%29%2B4%2Asqrt%2898x%5E2%29-3x%2Asqrt%28162x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13x%2Asqrt%282x%29%2B28x%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"13x%2Asqrt%282x%29%2B28x%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Or we can say<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2Asqrt%28128x%5E3%29%2B4%2Asqrt%2898x%5E2%29-3x%2Asqrt%28162x%29=13x%2Asqrt%282x%29%2B28x%2Asqrt%282%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "only when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3E=+0 ALIGN=MIDDLE  ALT=\"x+%3E=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );