document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=118061>Question 118061</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use the properties for radicals to simplify each of the following expressions. Assume that all variables represent positive real numbers.\r<BR>\n" );
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document.write( "1. square root of 5/3\r<BR>\n" );
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document.write( "2. square root of 12x cubed/5 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #86138 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=86138\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> #1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%285%2F3%29 ALIGN=MIDDLE  ALT=\"sqrt%285%2F3%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%285%29%2Fsqrt%283%29 ALIGN=MIDDLE  ALT=\"sqrt%285%29%2Fsqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the square root\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%285%29%2Fsqrt%283%29%29%28sqrt%283%29%2Fsqrt%283%29%29 ALIGN=MIDDLE  ALT=\"%28sqrt%285%29%2Fsqrt%283%29%29%28sqrt%283%29%2Fsqrt%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the fraction by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%29%2Fsqrt%283%29 ALIGN=MIDDLE  ALT=\"sqrt%283%29%2Fsqrt%283%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=%28sqrt%285%29sqrt%283%29%29%2F%28sqrt%283%29sqrt%283%29%29 ALIGN=MIDDLE  ALT=\"%28sqrt%285%29sqrt%283%29%29%2F%28sqrt%283%29sqrt%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the fraction\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%285%2A3%29%29%2F%28sqrt%283%2A3%29%29 ALIGN=MIDDLE  ALT=\"%28sqrt%285%2A3%29%29%2F%28sqrt%283%2A3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the roots\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2815%29%2Fsqrt%289%29 ALIGN=MIDDLE  ALT=\"sqrt%2815%29%2Fsqrt%289%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=sqrt%2815%29%2F3 ALIGN=MIDDLE  ALT=\"sqrt%2815%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of 9 to get 3. Notice how the denominator is a rational number. This is why I multiplied the fraction by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%29%2Fsqrt%283%29 ALIGN=MIDDLE  ALT=\"sqrt%283%29%2Fsqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "#2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2812x%5E3%2F5%29 ALIGN=MIDDLE  ALT=\"sqrt%2812x%5E3%2F5%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%2812x%5E3%29%2Fsqrt%285%29 ALIGN=MIDDLE  ALT=\"sqrt%2812x%5E3%29%2Fsqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the square root\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%2812x%5E3%29%2Fsqrt%285%29%29%28sqrt%285%29%2Fsqrt%285%29%29 ALIGN=MIDDLE  ALT=\"%28sqrt%2812x%5E3%29%2Fsqrt%285%29%29%28sqrt%285%29%2Fsqrt%285%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the fraction by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%285%29%2Fsqrt%285%29 ALIGN=MIDDLE  ALT=\"sqrt%285%29%2Fsqrt%285%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=%28sqrt%2812x%5E3%29sqrt%285%29%29%2F%28sqrt%285%29sqrt%285%29%29 ALIGN=MIDDLE  ALT=\"%28sqrt%2812x%5E3%29sqrt%285%29%29%2F%28sqrt%285%29sqrt%285%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the fraction\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%2812x%5E3%2A5%29%29%2F%28sqrt%285%2A5%29%29 ALIGN=MIDDLE  ALT=\"%28sqrt%2812x%5E3%2A5%29%29%2F%28sqrt%285%2A5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the roots\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2860x%5E3%29%2Fsqrt%2825%29 ALIGN=MIDDLE  ALT=\"sqrt%2860x%5E3%29%2Fsqrt%2825%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=sqrt%2860x%5E3%29%2F5 ALIGN=MIDDLE  ALT=\"sqrt%2860x%5E3%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of 25 to get 5. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%284%2A15x%5E2%2Ax%29%2F5 ALIGN=MIDDLE  ALT=\"sqrt%284%2A15x%5E2%2Ax%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor 60 into 4*15 <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3 ALIGN=MIDDLE  ALT=\"x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Ax ALIGN=MIDDLE  ALT=\"x%5E2%2Ax\"   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%284%29sqrt%2815%29sqrt%28x%5E2%29sqrt%28x%29%2F5 ALIGN=MIDDLE  ALT=\"sqrt%284%29sqrt%2815%29sqrt%28x%5E2%29sqrt%28x%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the root\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282sqrt%2815%29x%2Asqrt%28x%29%29%2F5 ALIGN=MIDDLE  ALT=\"%282sqrt%2815%29x%2Asqrt%28x%29%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get 2 and take the square root of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get x\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2Ax%2Asqrt%2815%29sqrt%28x%29%29%2F5 ALIGN=MIDDLE  ALT=\"%282%2Ax%2Asqrt%2815%29sqrt%28x%29%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%2Asqrt%2815x%29%29%2F5 ALIGN=MIDDLE  ALT=\"%282x%2Asqrt%2815x%29%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the roots\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2812x%5E3%2F5%29 ALIGN=MIDDLE  ALT=\"sqrt%2812x%5E3%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%2Asqrt%2815x%29%29%2F5 ALIGN=MIDDLE  ALT=\"%282x%2Asqrt%2815x%29%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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