document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=824332>Question 824332</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Express the ratio of the area of the larger circle to the area of the smaller circle in simplest radical form.<BR>\n" );
document.write( "Radius of larger circle is 2 + sqrt of 3<BR>\n" );
document.write( "Radius of smaller circle is 2 - sqrt of 3\r<BR>\n" );
document.write( "\n" );
document.write( "Advance Thanks to whoever answers :) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #496338 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3759)</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=496338\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The formula for area of a circle is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+pi%2Ar%5E2 ALIGN=MIDDLE  ALT=\"A+=+pi%2Ar%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So the area for the larger circle will be:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5BL%5D+=+pi%2A%282%2Bsqrt%283%29%29%5E2 ALIGN=MIDDLE  ALT=\"A%5BL%5D+=+pi%2A%282%2Bsqrt%283%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Using the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Bb%29%5E2+=+a%5E2%2B2ab%2Bb%5E2 ALIGN=MIDDLE  ALT=\"%28a%2Bb%29%5E2+=+a%5E2%2B2ab%2Bb%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > pattern to square the radius:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5BL%5D+=+pi%2A%28%282%29%5E2%2B2%282%29%28sqrt%283%29%29%2B%28sqrt%283%29%29%5E2%29 ALIGN=MIDDLE  ALT=\"A%5BL%5D+=+pi%2A%28%282%29%5E2%2B2%282%29%28sqrt%283%29%29%2B%28sqrt%283%29%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Simplifying...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5BL%5D+=+pi%2A%284%2B4sqrt%283%29%2B3%29 ALIGN=MIDDLE  ALT=\"A%5BL%5D+=+pi%2A%284%2B4sqrt%283%29%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5BL%5D+=+pi%2A%287%2B4sqrt%283%29%29 ALIGN=MIDDLE  ALT=\"A%5BL%5D+=+pi%2A%287%2B4sqrt%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Repeating this for the smaller circle:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5BS%5D+=+pi%2A%282-sqrt%283%29%29%5E2 ALIGN=MIDDLE  ALT=\"A%5BS%5D+=+pi%2A%282-sqrt%283%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Using the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a-b%29%5E2+=+a%5E2-2ab%2Bb%5E2 ALIGN=MIDDLE  ALT=\"%28a-b%29%5E2+=+a%5E2-2ab%2Bb%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > pattern to square the radius:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5BS%5D+=+pi%2A%28%282%29%5E2-2%282%29%28sqrt%283%29%29%2B%28sqrt%283%29%29%5E2%29 ALIGN=MIDDLE  ALT=\"A%5BS%5D+=+pi%2A%28%282%29%5E2-2%282%29%28sqrt%283%29%29%2B%28sqrt%283%29%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Simplifying...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5BS%5D+=+pi%2A%284-4sqrt%283%29%2B3%29 ALIGN=MIDDLE  ALT=\"A%5BS%5D+=+pi%2A%284-4sqrt%283%29%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5BS%5D+=+pi%2A%287-4sqrt%283%29%29 ALIGN=MIDDLE  ALT=\"A%5BS%5D+=+pi%2A%287-4sqrt%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Now we find the ratio of these areas:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5BL%5D%2FA%5BS%5D+=+%28pi%2A%287%2B4sqrt%283%29%29%29%2F%28pi%2A%287-4sqrt%283%29%29%29 ALIGN=MIDDLE  ALT=\"A%5BL%5D%2FA%5BS%5D+=+%28pi%2A%287%2B4sqrt%283%29%29%29%2F%28pi%2A%287-4sqrt%283%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Simplifying... The <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi ALIGN=MIDDLE  ALT=\"pi\"   DISABLED_style= \"max-width:90%; height:auto;\" >'s cancel:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5BL%5D%2FA%5BS%5D+=+%287%2B4sqrt%283%29%29%2F%287-4sqrt%283%29%29 ALIGN=MIDDLE  ALT=\"A%5BL%5D%2FA%5BS%5D+=+%287%2B4sqrt%283%29%29%2F%287-4sqrt%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This may be an acceptable answer.<br><BR>\n" );
document.write( "But it does have a square root in the denominator. Usually denominators should be rationalized:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5BL%5D%2FA%5BS%5D+=+%28%287%2B4sqrt%283%29%29%2F%287-4sqrt%283%29%29%29%28%287%2B4sqrt%283%29%29%2F%287%2B4sqrt%283%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Using the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Bb%29%5E2 ALIGN=MIDDLE  ALT=\"%28a%2Bb%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > pattern on top and the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Bb%29%28a-b%29=a%5E2-b%5E2 ALIGN=MIDDLE  ALT=\"%28a%2Bb%29%28a-b%29=a%5E2-b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > pattern on the bottom:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5BL%5D%2FA%5BS%5D+=+%28%287%29%5E2%2B2%287%29%284sqrt%283%29%29%2B%284sqrt%283%29%29%5E2%29%2F%28%287%29%5E2-%284sqrt%283%29%29%5E2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Simplifying...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5BL%5D%2FA%5BS%5D+=+%2849%2B56sqrt%283%29%2B48%29%2F%2849-48%29 ALIGN=MIDDLE  ALT=\"A%5BL%5D%2FA%5BS%5D+=+%2849%2B56sqrt%283%29%2B48%29%2F%2849-48%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5BL%5D%2FA%5BS%5D+=+%2897%2B56sqrt%283%29%29%2F1 ALIGN=MIDDLE  ALT=\"A%5BL%5D%2FA%5BS%5D+=+%2897%2B56sqrt%283%29%29%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5BL%5D%2FA%5BS%5D+=+97%2B56sqrt%283%29 ALIGN=MIDDLE  ALT=\"A%5BL%5D%2FA%5BS%5D+=+97%2B56sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );