document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=76330>Question 76330</A>: <I><SPAN STYLE=\"word-break: break-all;\"> d..\r<BR>\n" );
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document.write( "Problem #1<BR>\n" );
document.write( "Can someone explain to me if the following is rational or irrational and why?\r<BR>\n" );
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document.write( "minus then an index of 4 sqrt 16\r<BR>\n" );
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document.write( "Problem #2\r<BR>\n" );
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document.write( "Simplify. Assuming all variables represents positive numbers\r<BR>\n" );
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document.write( "sqrt (x^4y^3) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #54768 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=54768\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Problem #1\r<BR>\n" );
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document.write( "If we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-root%284%2C16%29 ALIGN=MIDDLE  ALT=\"-root%284%2C16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then we are asking: what number multiplied by itself 4 times equals 16? In other words:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Ax%2Ax%2Ax=x%5E4=16 ALIGN=MIDDLE  ALT=\"x%2Ax%2Ax%2Ax=x%5E4=16\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So if we take the negative fourth root of 16 with a calculator, we get \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-root%284%2C16%29=-2 ALIGN=MIDDLE  ALT=\"-root%284%2C16%29=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since -2 can be represented by a fraction (ie <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2=-2%2F1 ALIGN=MIDDLE  ALT=\"-2=-2%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" >) it is a rational number.\r<BR>\n" );
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document.write( "Problem #2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt+%28x%5E4y%5E3%29 ALIGN=MIDDLE  ALT=\"sqrt+%28x%5E4y%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt+%28x%5E4%29%2Asqrt%28y%5E3%29 ALIGN=MIDDLE  ALT=\"sqrt+%28x%5E4%29%2Asqrt%28y%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite the square root of a product as a product of square roots (ie <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28xy%29=sqrt%28x%29sqrt%28y%29 ALIGN=MIDDLE  ALT=\"sqrt%28xy%29=sqrt%28x%29sqrt%28y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E4%29%5E%281%2F2%29%2A%28y%5E3%29%5E%281%2F2%29 ALIGN=MIDDLE  ALT=\"%28x%5E4%29%5E%281%2F2%29%2A%28y%5E3%29%5E%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >Since any root can be written as a fractional power (ie <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%28n%2Cx%29=x%5E%281%2Fn%29 ALIGN=MIDDLE  ALT=\"root%28n%2Cx%29=x%5E%281%2Fn%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > rewrite the square roots as exponents of 1/2.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E%284%2A%281%2F2%29%29%29%2A%28y%5E%283%2A%281%2F2%29%29%29 ALIGN=MIDDLE  ALT=\"%28x%5E%284%2A%281%2F2%29%29%29%2A%28y%5E%283%2A%281%2F2%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the exponents<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%29%2A%28y%5E%28%283%2F2%29%29%29 ALIGN=MIDDLE  ALT=\"%28x%5E2%29%2A%28y%5E%28%283%2F2%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > So this is your simplified answer. It can also be written as:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%29%2Asqrt%28y%5E3%29%29%29 ALIGN=MIDDLE  ALT=\"%28x%5E2%29%2Asqrt%28y%5E3%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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