document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=182180>Question 182180</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the real solutions of each equation.\r<BR>\n" );
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document.write( "31. the sqrt of 10 + 3 and within this sqrt is the sqrt of x = the sqrt of x\r<BR>\n" );
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document.write( "33. (3x +1) to the power of 1/2 = 4\r<BR>\n" );
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document.write( "39. x to the power of 3/2 - 3x to the power of 1/2 = 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #136816 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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/cgi-bin/show-face.mpl?user=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=136816\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "31.  I think you mean:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math sqrt{10 + 3 \sqrt{x}}=sqrt{x}\">\r<BR>\n" );
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document.write( "Square both sides:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math 10 + 3 sqrt{x}= x \">\r<BR>\n" );
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document.write( "Add -10 to both sides:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math 3 sqrt{x}= x - 10\">\r<BR>\n" );
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document.write( "Square both sides:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math 9x = x^2 - 20x + 100\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math  x^2 - 29x + 100 = 0\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math  (x - 4)(x - 25) = 0\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math  x = 4 \text{ or } \math x = 25\">\r<BR>\n" );
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document.write( "Check answers:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math sqrt{10 + 3 \sqrt{4}}=?sqrt{4}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math sqrt{16}\neq sqrt{4}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math  x = 4 \"> is extraneous\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math sqrt{10 + 3 \sqrt{25}}=?sqrt{25}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math sqrt{25}=sqrt{25}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math  x = 25 \"> is valid.\r<BR>\n" );
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document.write( "33. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math  (3x +1)^{\frac{1}{2}} = 4\">\r<BR>\n" );
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document.write( "This is exactly the same as:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math  sqrt{3x +1} = 4\">\r<BR>\n" );
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document.write( "Just square both sides and solve.\r<BR>\n" );
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document.write( "39.  Two possible interpretations:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{(1)          }\math  x^{3 \over 2} - 3x^{1 \over 2} = 0\ \ \Rightarrow\ \ x^{3 \over 2} = 3x^{1 \over 2} \cr \text{      }\math\ \ \Rightarrow\ \ x^3 = 3x \ \ \Rightarrow\ \ x^2 = 3\ \ \Rightarrow\ \ x = \pm sqrt{3}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{(2)          }\math  x^{3 \over 2} - (3x)^{1 \over 2} = 0\ \ \Rightarrow\ \ x^{3 \over 2} = (3x)^{1 \over 2} \cr \text{      }\math\ \ \Rightarrow\ \ x^3 = 9x \ \ \Rightarrow\ \ x^2 = 9\ \ \Rightarrow\ \ x = \pm 3\">\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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