document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=340427>Question 340427</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the simplified radical form of 3087?<BR>\n" );
document.write( "I factored this number  by three two times but I am stuck on 343 becuase I don't know what numbers it is divisible by.<BR>\n" );
document.write( "       3087<BR>\n" );
document.write( "      3 1029<BR>\n" );
document.write( "          3   343\r<BR>\n" );
document.write( "\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 #243954 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=243954\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283087%29 ALIGN=MIDDLE  ALT=\"sqrt%283087%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The goal of simplifying expressions with square roots is to factor the radicand into a product of two numbers. One of these two numbers must be a perfect square. When you take the square root of this perfect square, you will get a rational number.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So let's list the factors of 3087\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Factors:\r<BR>\n" );
document.write( "\n" );
document.write( "1, 3, 7, 9, 21, 49, 63, 147, 343, 441, 1029, 3087\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Notice how 441 is the largest perfect square, so lets factor 3087 into 441*7\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28441%2A7%29 ALIGN=MIDDLE  ALT=\"sqrt%28441%2A7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor 3087 into 441*7<BR>\n" );
document.write( " \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28441%29%2Asqrt%287%29 ALIGN=MIDDLE  ALT=\"sqrt%28441%29%2Asqrt%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the square roots using the identity <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21%2Asqrt%287%29 ALIGN=MIDDLE  ALT=\"21%2Asqrt%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of the perfect square 441 to get 21 <BR>\n" );
document.write( " \r<BR>\n" );
document.write( "\n" );
document.write( "So the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283087%29 ALIGN=MIDDLE  ALT=\"sqrt%283087%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21%2Asqrt%287%29 ALIGN=MIDDLE  ALT=\"21%2Asqrt%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "----------------------------<BR>\n" );
document.write( "Check:\r<BR>\n" );
document.write( "\n" );
document.write( "Notice if we evaluate the square root of 3087 with a calculator we get\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283087%29=55.5607775323564 ALIGN=MIDDLE  ALT=\"sqrt%283087%29=55.5607775323564\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "and if we evaluate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21%2Asqrt%287%29 ALIGN=MIDDLE  ALT=\"21%2Asqrt%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > we get\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21%2Asqrt%287%29=55.5607775323564 ALIGN=MIDDLE  ALT=\"21%2Asqrt%287%29=55.5607775323564\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This shows that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283087%29=21%2Asqrt%287%29 ALIGN=MIDDLE  ALT=\"sqrt%283087%29=21%2Asqrt%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So this verifies our answer \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If you need more help, email me at <a  rel=nofollow HREF=\"mailto:jim_thompson5910@hotmail.com?Subject=Algebra%20Help\">jim_thompson5910@hotmail.com</a>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Also, feel free to check out my <a  rel=nofollow HREF=\"http://www.freewebs.com/jimthompson5910/home.html\">tutoring website</a>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Jim </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );