document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=395159>Question 395159</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 3 &#8732; 24<BR>\n" );
document.write( "multiplied by<BR>\n" );
document.write( "5  &#8732; 2\r<BR>\n" );
document.write( "\n" );
document.write( "why is the answer 30 &#8732;3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #280538 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=280538\">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=3%2Aroot%284%2C+24%29%2A5%2Aroot%284%2C+2%29 ALIGN=MIDDLE  ALT=\"3%2Aroot%284%2C+24%29%2A5%2Aroot%284%2C+2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is all multiplication. So we can use the Commutative and Associative Properties to rearrange the order and grouping in any way we choose:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2A5%29%2A%28root%284%2C+24%29%2Aroot%284%2C+2%29%29 ALIGN=MIDDLE  ALT=\"%283%2A5%29%2A%28root%284%2C+24%29%2Aroot%284%2C+2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "To multiply the radicals we use the property of all radicals: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%28a%2C+p%29%2Aroot%28a%2C+q%29+=+root%28a%2C+p%2Aq%29 ALIGN=MIDDLE  ALT=\"root%28a%2C+p%29%2Aroot%28a%2C+q%29+=+root%28a%2C+p%2Aq%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2Aroot%284%2C+24%2A2%29 ALIGN=MIDDLE  ALT=\"15%2Aroot%284%2C+24%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2Aroot%284%2C+48%29 ALIGN=MIDDLE  ALT=\"15%2Aroot%284%2C+48%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Just like fractions should be reduced, radicals should be simplified. Simplifying radicals involves finding factors of the radicand (the expression within a radical) that are powers of the type of root, if any. In this problem with its 4th root, we are looking for factors of 48 that are a power of 4. Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E4+=+16 ALIGN=MIDDLE  ALT=\"2%5E4+=+16\"   DISABLED_style= \"max-width:90%; height:auto;\" > and since 16 is a factor of 48, this radical will simplify. We start by writing the radicand in factored form:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2Aroot%284%2C+16%2A3%29 ALIGN=MIDDLE  ALT=\"15%2Aroot%284%2C+16%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then we use the property of radicals we used earlier. Only this time we use it in the other direction: to split a single radical into a product of radicals. By doing this we get the power of 4 factor into its own radical:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2Aroot%284%2C+16%29%2Aroot%284%2C+3%29 ALIGN=MIDDLE  ALT=\"15%2Aroot%284%2C+16%29%2Aroot%284%2C+3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The 4th root of 16 is 2 so this becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2A2%2Aroot%284%2C+3%29 ALIGN=MIDDLE  ALT=\"15%2A2%2Aroot%284%2C+3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which simplifies to<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30%2Aroot%284%2C+3%29 ALIGN=MIDDLE  ALT=\"30%2Aroot%284%2C+3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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