document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=142182>Question 142182</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help with the following question. Thank you\r<BR>\n" );
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document.write( "square root of x multiplied by the 4th root of x+4.  I am to use Rational exponents to wrtie a single radical expression.\r<BR>\n" );
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document.write( "Thanks so much </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #103517 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=103517\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%29%2Aroot%284%2Cx%2B4%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%29%2Aroot%284%2Cx%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%29%2A%28x%2B4%29%5E%281%2F4%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%29%2A%28x%2B4%29%5E%281%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%284%2Cx%2B4%29 ALIGN=MIDDLE  ALT=\"root%284%2Cx%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B4%29%5E%281%2F4%29 ALIGN=MIDDLE  ALT=\"%28x%2B4%29%5E%281%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%29%2A%28%28x%2B4%29%5E%281%2F2%29%29%5E%281%2F2%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%29%2A%28%28x%2B4%29%5E%281%2F2%29%29%5E%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B4%29%5E%281%2F4%29 ALIGN=MIDDLE  ALT=\"%28x%2B4%29%5E%281%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%2B4%29%5E%281%2F2%29%29%5E%281%2F2%29 ALIGN=MIDDLE  ALT=\"%28%28x%2B4%29%5E%281%2F2%29%29%5E%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Notice how <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%2B4%29%5E%281%2F2%29%29%5E%281%2F2%29=%28x%2B4%29%5E%28%281%2F2%29%281%2F2%29%29+=%28x%2B4%29%5E%281%2F4%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%29%2Asqrt%28%28x%2B4%29%5E%281%2F2%29%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%29%2Asqrt%28%28x%2B4%29%5E%281%2F2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%2B4%29%5E%281%2F2%29%29%5E%281%2F2%29 ALIGN=MIDDLE  ALT=\"%28%28x%2B4%29%5E%281%2F2%29%29%5E%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28x%2B4%29%5E%281%2F2%29%29 ALIGN=MIDDLE  ALT=\"sqrt%28%28x%2B4%29%5E%281%2F2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%29%2Asqrt%28sqrt%28x%2B4%29%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%29%2Asqrt%28sqrt%28x%2B4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B4%29%5E%281%2F2%29 ALIGN=MIDDLE  ALT=\"%28x%2B4%29%5E%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%2B4%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%2Asqrt%28x%2B4%29%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%2Asqrt%28x%2B4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the square roots.\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%29%2Aroot%284%2Cx%2B4%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%29%2Aroot%284%2Cx%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%2Asqrt%28x%2B4%29%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%2Asqrt%28x%2B4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "If you want you can go further and do...\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28sqrt%28x%5E2%29%2Asqrt%28x%2B4%29%29 ALIGN=MIDDLE  ALT=\"sqrt%28sqrt%28x%5E2%29%2Asqrt%28x%2B4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28sqrt%28x%5E2%28x%2B4%29%29%29 ALIGN=MIDDLE  ALT=\"sqrt%28sqrt%28x%5E2%28x%2B4%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the inner square roots\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%5E2%28x%2B4%29%29%5E%281%2F2%29%29%5E%281%2F2%29 ALIGN=MIDDLE  ALT=\"%28%28x%5E2%28x%2B4%29%29%5E%281%2F2%29%29%5E%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite each square root as a rational exponent\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%28x%2B4%29%29%5E%28%281%2F2%29%281%2F2%29%29 ALIGN=MIDDLE  ALT=\"%28x%5E2%28x%2B4%29%29%5E%28%281%2F2%29%281%2F2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the exponents\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%28x%2B4%29%29%5E%281%2F4%29 ALIGN=MIDDLE  ALT=\"%28x%5E2%28x%2B4%29%29%5E%281%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%284%2Cx%5E2%28x%2B4%29%29 ALIGN=MIDDLE  ALT=\"root%284%2Cx%5E2%28x%2B4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Convert the rational expression to a radical expression\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%284%2Cx%5E3%2B4x%5E2%29 ALIGN=MIDDLE  ALT=\"root%284%2Cx%5E3%2B4x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%29%2Aroot%284%2Cx%2B4%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%29%2Aroot%284%2Cx%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > also simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%284%2Cx%5E3%2B4x%5E2%29 ALIGN=MIDDLE  ALT=\"root%284%2Cx%5E3%2B4x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <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;\" > </SPAN>\n" );
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