document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=149817>Question 149817</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Is sqrt of a + sqrt of b = sqrt a+b for all values of a and b? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #109929 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=109929\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's assume that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28a%29%2Bsqrt%28b%29=sqrt%28a%2Bb%29 ALIGN=MIDDLE  ALT=\"sqrt%28a%29%2Bsqrt%28b%29=sqrt%28a%2Bb%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > for all values of a and b. So now let's just pick arbitrary values for a and b. So let's make <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=2 ALIGN=MIDDLE  ALT=\"a=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=3 ALIGN=MIDDLE  ALT=\"b=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28a%29%2Bsqrt%28b%29=sqrt%28a%2Bb%29 ALIGN=MIDDLE  ALT=\"sqrt%28a%29%2Bsqrt%28b%29=sqrt%28a%2Bb%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%29%2Bsqrt%283%29=sqrt%282%2B3%29 ALIGN=MIDDLE  ALT=\"sqrt%282%29%2Bsqrt%283%29=sqrt%282%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=2 ALIGN=MIDDLE  ALT=\"a=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=3 ALIGN=MIDDLE  ALT=\"b=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%29%2Bsqrt%283%29=sqrt%285%29 ALIGN=MIDDLE  ALT=\"sqrt%282%29%2Bsqrt%283%29=sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 2 and 3 to get 5\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.41421%2B1.73205=2.23607 ALIGN=MIDDLE  ALT=\"1.41421%2B1.73205=2.23607\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of 2 to get 1.41421. Take the square root of 3 to get 1.73205. Take the square root of 5 to get 2.23607.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3.14626=2.23607 ALIGN=MIDDLE  ALT=\"3.14626=2.23607\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 1.41421 and 1.73205 to get 3.14626\r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3.14626%3C%3E2.23607 ALIGN=MIDDLE  ALT=\"3.14626%3C%3E2.23607\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this shows us that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%29%2Bsqrt%283%29%3C%3Esqrt%282%2B3%29 ALIGN=MIDDLE  ALT=\"sqrt%282%29%2Bsqrt%283%29%3C%3Esqrt%282%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "So this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28a%29%2Bsqrt%28b%29%3C%3Esqrt%28a%2Bb%29 ALIGN=MIDDLE  ALT=\"sqrt%28a%29%2Bsqrt%28b%29%3C%3Esqrt%28a%2Bb%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. There are some values that will make it true. For instance <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=0 ALIGN=MIDDLE  ALT=\"a=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=0 ALIGN=MIDDLE  ALT=\"b=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > are one pair of values, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1 ALIGN=MIDDLE  ALT=\"a=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=0 ALIGN=MIDDLE  ALT=\"b=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > are another. However, in general, the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28a%29%2Bsqrt%28b%29=sqrt%28a%2Bb%29 ALIGN=MIDDLE  ALT=\"sqrt%28a%29%2Bsqrt%28b%29=sqrt%28a%2Bb%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is not true. </SPAN>\n" );
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