document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=327571>Question 327571</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need some help with some problems, hope you could help me.  I am not that good in algebra, so I need help with the following.\r<BR>\n" );
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document.write( "1.  Find all numbers for which the rational expression is undefined.\r<BR>\n" );
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document.write( "q^3-7q over q^2-64 (fraction).\r<BR>\n" );
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document.write( "2.  Multiply & simplify by factoring.  Assume that all expressions under radicals represent nonnegative numbers.  3(small three) sqrt y^4 3(small) sqrt 81y^5.\r<BR>\n" );
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document.write( "3.  Use rational exponents to simplify  5sqrtx^15\r<BR>\n" );
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document.write( "4.For the following equation, state the value of the dicriminant & then describe the nature of the solutions.  -16x^2+3x-3=0  What is the value of the discriminant?\r<BR>\n" );
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document.write( "5.  Find the following: sqrt(a+6)^2.  Assume that variables can represent any real number. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #234611 by </B><A HREF=/tutors/aboutme.mpl?userid=ganeshindia><B>ganeshindia(11)</B></A><img src=\"/images/stars/stars-06.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ganeshindia><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=234611\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1) All numbers for which the rational expression <BR>\n" );
document.write( "(q^3-7q)/(q^2-64)is undefined.<BR>\n" );
document.write( "Solution:<BR>\n" );
document.write( "     The above rational expression is undefined when the denominator becomes zero. That is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q%5E2+-+64=0 ALIGN=MIDDLE  ALT=\"q%5E2+-+64=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "That is , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q%5E2+=+64. ALIGN=MIDDLE  ALT=\"q%5E2+=+64.\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "q = + or - {sqrt of 64}<BR>\n" );
document.write( "q = +8 or q= -8. <BR>\n" );
document.write( "The rational expression is undefined for q = +8 and q= -8.\r<BR>\n" );
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document.write( "3) Use rational exponents to simplify <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5sqrtx%5E15+. ALIGN=MIDDLE  ALT=\"5sqrtx%5E15+.\"   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=5th+root+of+x%5E15+=+%28x%5E15%29%5E%281%2F5%29 ALIGN=MIDDLE  ALT=\"5th+root+of+x%5E15+=+%28x%5E15%29%5E%281%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "                 = (x^3)^5)^(1/5)<BR>\n" );
document.write( "                 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3 ALIGN=MIDDLE  ALT=\"x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "4)For the following equation, state the value of the discriminant & then describe the nature of the solutions. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16x%5E2%2B3x-3=0 ALIGN=MIDDLE  ALT=\"-16x%5E2%2B3x-3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > What is the value of the discriminant? <BR>\n" );
document.write( "Sol: <BR>\n" );
document.write( "For the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2+%2B+bx+%2B+c+=+0 ALIGN=MIDDLE  ALT=\"ax%5E2+%2B+bx+%2B+c+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, The discriminant value is b^2 - 4ac.<BR>\n" );
document.write( "From the given equation, we get a = -16, b = 3 and c = -3.<BR>\n" );
document.write( "Therefore,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b%5E2+-+4ac+=+3%5E2+-+4%28-16%29%28-3%29+=+9+%2B+192+=+201. ALIGN=MIDDLE  ALT=\"+b%5E2+-+4ac+=+3%5E2+-+4%28-16%29%28-3%29+=+9+%2B+192+=+201.\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We get, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2+-+4ac+%3E+0. ALIGN=MIDDLE  ALT=\"b%5E2+-+4ac+%3E+0.\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Therefore the roots are real, unequal and irrational. <BR>\n" );
document.write( " </SPAN>\n" );
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