document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=116380>Question 116380</A>: <I><SPAN STYLE=\"word-break: break-all;\"> radical 50 + radical 18 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #84619 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=84619\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You are given:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2850%29+%2B+sqrt%2818%29 ALIGN=MIDDLE  ALT=\"sqrt%2850%29+%2B+sqrt%2818%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "To simplify this you can use the rule that says:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28A%2AB%29+=+sqrt%28A%29%2Asqrt%28B%29 ALIGN=MIDDLE  ALT=\"sqrt%28A%2AB%29+=+sqrt%28A%29%2Asqrt%28B%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Applying that rule to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2850%29 ALIGN=MIDDLE  ALT=\"sqrt%2850%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > we can break the 50 up into the product of 25*2.<BR>\n" );
document.write( "So we can say that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2850%29+=+sqrt%2825%2A2%29+=+sqrt%2825%29%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"sqrt%2850%29+=+sqrt%2825%2A2%29+=+sqrt%2825%29%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "But <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2825%29+=+5 ALIGN=MIDDLE  ALT=\"sqrt%2825%29+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So we can substitute 5 for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2825%29 ALIGN=MIDDLE  ALT=\"sqrt%2825%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the problem simplifies<BR>\n" );
document.write( "further:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2850%29+=+sqrt%2825%2A2%29+=+sqrt%2825%29%2Asqrt%282%29+=+5%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"sqrt%2850%29+=+sqrt%2825%2A2%29+=+sqrt%2825%29%2Asqrt%282%29+=+5%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Now let's do the same thing for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2818%29 ALIGN=MIDDLE  ALT=\"sqrt%2818%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Factor 18 so that you have:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2818%29+=+sqrt%289%2A2%29+=+sqrt%289%29%2A+sqrt%282%29 ALIGN=MIDDLE  ALT=\"sqrt%2818%29+=+sqrt%289%2A2%29+=+sqrt%289%29%2A+sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "And <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%289%29+=+3 ALIGN=MIDDLE  ALT=\"sqrt%289%29+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > so this part of the problem simplifies further to:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2818%29+=+sqrt%289%2A2%29+=+sqrt%289%29%2A+sqrt%282%29+=+3%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"sqrt%2818%29+=+sqrt%289%2A2%29+=+sqrt%289%29%2A+sqrt%282%29+=+3%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Put the two parts of the problem together ...<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2850%29+%2B+sqrt%2818%29+=+5%2Asqrt%282%29+%2B+3%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"sqrt%2850%29+%2B+sqrt%2818%29+=+5%2Asqrt%282%29+%2B+3%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "If you factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%29 ALIGN=MIDDLE  ALT=\"sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > from the two terms on the right side you get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2Asqrt%282%29+%2B+3%2Asqrt%282%29+=+%285+%2B+3%29%2Asqrt%282%29+=+8%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"5%2Asqrt%282%29+%2B+3%2Asqrt%282%29+=+%285+%2B+3%29%2Asqrt%282%29+=+8%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "So the answer to this problem is:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2850%29+%2B+sqrt%2818%29+=+8%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"sqrt%2850%29+%2B+sqrt%2818%29+=+8%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Hope this helps you to understand one of the rules that can be used in simplifying <BR>\n" );
document.write( "radicals.<BR>\n" );
document.write( ". </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );