document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=527530>Question 527530</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please help me solve this problem i do not understand what they mean. If the square root of a number is a repeating decimal, is the square root a rational number?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #349105 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=349105\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Yes. Repeating decimals are rational numbers, so the square root of the number, and the number itself, are rational.\r<BR>\n" );
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document.write( "To prove that a repeating decimal is rational, you can treat an iterating \"string\" of digits as a term of a geometric series. For example, if your repeating decimal is 0.034034034... you can let the \"string\" be 034, in which the corresponding geometric series would be\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \sum_{i=1}^{\infty} 34(10^{-3k})\">\r<BR>\n" );
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document.write( "If you know the formula for the sum of a convergent geometric series, you can conclude that this is rational. </SPAN>\n" );
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