document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=425297>Question 425297</A>: <I><SPAN STYLE=\"word-break: break-all;\"> simplify the radical exspression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5sqrt%2824%29+multiply+by+3sqrt%2810%29 ALIGN=MIDDLE  ALT=\"5sqrt%2824%29+multiply+by+3sqrt%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #296235 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=296235\">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=5sqrt%2824%29%2A3sqrt%2810%29 ALIGN=MIDDLE  ALT=\"5sqrt%2824%29%2A3sqrt%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "When multiplying radicals you can either<ul><li>Simplify the radicals, multiply and then simplify the multiplied radical; or</li><li>Multiply and then simplify the radical.</li></ul><BR>\n" );
document.write( "Even though the first approach has two simplifications instead of just une, it can actually be easier this way when the expressions are complex. Your expression is not very complex so we will use the second approach.<br><BR>\n" );
document.write( "Sine the expression is all multiplications, we can use the Commutative and Associative Properties to rearrange the order and grouping:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2A3%29%28sqrt%2824%29%2Asqrt%2810%29%29 ALIGN=MIDDLE  ALT=\"%285%2A3%29%28sqrt%2824%29%2Asqrt%2810%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This first group, 5*3, is 3rd grade multiplication. To multiply the square roots we use a property of 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;\" >, to multiply. SO we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2Asqrt%2824%2A10%29 ALIGN=MIDDLE  ALT=\"15%2Asqrt%2824%2A10%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%2Asqrt%28240%29 ALIGN=MIDDLE  ALT=\"15%2Asqrt%28240%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Now we simplify the square roots we look for perfect square factors of the radicand. (The expression inside a radical is called a radicand.) 240 definitely has one (or more) perfect square factors:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2Asqrt%284%2A60%29 ALIGN=MIDDLE  ALT=\"15%2Asqrt%284%2A60%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "60 also has a prefect square factor:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2Asqrt%284%2A4%2A15%29 ALIGN=MIDDLE  ALT=\"15%2Asqrt%284%2A4%2A15%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we use the same property of radicals we used earlier, only in reverse, to split up the square root:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2Asqrt%284%29%2Asqrt%284%29%2A15%29 ALIGN=MIDDLE  ALT=\"15%2Asqrt%284%29%2Asqrt%284%29%2A15%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The square roots of the perfect squares simplify:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2A2%2A2%2A15%29 ALIGN=MIDDLE  ALT=\"15%2A2%2A2%2A15%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=60sqrt%2815%29 ALIGN=MIDDLE  ALT=\"60sqrt%2815%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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