document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=964354>Question 964354</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do you solve this? :  sqrt(1-a^2) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #589268 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=589268\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> this is not an equation.<BR>\n" );
document.write( "it's an expression.<BR>\n" );
document.write( "as an equation it would have to be equal to something, like sqrt(1-a^2) = 5.<BR>\n" );
document.write( "by itself it has no solution.<BR>\n" );
document.write( "the best you can do is find the values of a that would make the solution real.<BR>\n" );
document.write( "since the square root of a number has to be greater than or equal to 0, then you get:<BR>\n" );
document.write( "1 - a^2 >= 0<BR>\n" );
document.write( "add a^2 to both sides of that equation to get 1 >= a^2<BR>\n" );
document.write( "that's the same as a^2 <= 1<BR>\n" );
document.write( "in order for the solution to be real, a^2 must be smaller than or equal to 1.<BR>\n" );
document.write( "when does that happen?<BR>\n" );
document.write( "set a^2 equal to 1.<BR>\n" );
document.write( "solve for a by taking the square root of both sides of this equation to get:<BR>\n" );
document.write( "a = plus or minus sqrt(1) which becomes a = plus or minus 1.<BR>\n" );
document.write( "so a^2 = 1 when a is equal to plus or minus 1.<BR>\n" );
document.write( "what happens when a is greater than 1.<BR>\n" );
document.write( "a^2 is greater than 1, so a can't be greater than 1.<BR>\n" );
document.write( "what happens when is is smaller than -1.<BR>\n" );
document.write( "a^2 is greater t han 1, so a can't be smaller than -1.<BR>\n" );
document.write( "that happens when a is between -1 and 1.<BR>\n" );
document.write( "a^2 is less than 1.<BR>\n" );
document.write( "bottom line is -1 <= a <= 1 is when the solution will be real because a^2 will then be less than or equal to 1 and the square root of (1-a^2) will therefore be greater than or equal to 0.\r<BR>\n" );
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