document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=41260>Question 41260</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Radical expressions<BR>\n" );
document.write( "Three students were asked to simplify sqrt10 +sqrt50. Their answers were:<BR>\n" );
document.write( "Sqrt10(1+sqrt5),<BR>\n" );
document.write( "Sqrt10+5sqrt2, and<BR>\n" );
document.write( "Sqrt2(5+sqrt5).<BR>\n" );
document.write( "Which if any is correct?<BR>\n" );
document.write( "Which is in simplest form?<BR>\n" );
document.write( "Thanks so much </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #26636 by </B><A HREF=/tutors/aboutme.mpl?userid=zeynep><B>zeynep(43)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=zeynep><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=26636\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> sqrt10+sqrt50<BR>\n" );
document.write( "sqrt 50= sqrt10.sqrt5<BR>\n" );
document.write( "so,\r<BR>\n" );
document.write( "\n" );
document.write( "sqrt10+sqrt50 = sqrt10+sqrt10.sqrt5 \r<BR>\n" );
document.write( "\n" );
document.write( "since sqrt10 is the common factor, we can write;\r<BR>\n" );
document.write( "\n" );
document.write( "sqrt10+sqrt50 = sqrt10+sqrt10.sqrt5 = sqrt10(1+sqrt5)<BR>\n" );
document.write( "So , the first answer you sent is right.\r<BR>\n" );
document.write( "\n" );
document.write( "Let's talk about the second answer;\r<BR>\n" );
document.write( "\n" );
document.write( "sqrt50 = sqrt 25.2= sqrt25.sqrt2 = 5.sqrt2 (Here we used that sqrt25 equals to 5)<BR>\n" );
document.write( "So,\r<BR>\n" );
document.write( "\n" );
document.write( "sqrt10+sqrt50 = sqrt10+5.sqrt2 \r<BR>\n" );
document.write( "\n" );
document.write( "Therefore, your second answer is right, too.\r<BR>\n" );
document.write( "\n" );
document.write( "When it comes to the last answer you sent;\r<BR>\n" );
document.write( "\n" );
document.write( "sqrt10+sqrt50 = sqrt2.5 + sqrt 25.2= sqrt2.sqrt5+sqrt25.sqrt2 =\r<BR>\n" );
document.write( "\n" );
document.write( "sqrt2.sqrt5 + 5.sqrt2 = sqrt2(sqrt5+5) (For the last step we factored out the common factor which was sqrt2.)\r<BR>\n" );
document.write( "\n" );
document.write( "So, your last answer is also right.\r<BR>\n" );
document.write( "\n" );
document.write( "I think first answer and last answer are in th simplest forms. However answer 2 can be simplified more. Actually answer 3 is the simplified form of answer 2.  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );