document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=303313>Question 303313</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please Help, I am confused about how to work with third roots.\r<BR>\n" );
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document.write( "I am supposed to multiply then simplify by factoring. <BR>\n" );
document.write( "(3rd root)of y^7 * (3rd root) of 16y^8\r<BR>\n" );
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document.write( "Use Rational exponents to simplify the third root of x^6\r<BR>\n" );
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document.write( "Find the 16th root of (-8)^16\r<BR>\n" );
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document.write( "Rewrite the 4th root of 23 with a rational exponent. \r<BR>\n" );
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document.write( "Simplify the 3rd root of -1/64\r<BR>\n" );
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document.write( "Simplify by taking roots of the numerator and denominator<BR>\n" );
document.write( "(3rd root) of 1000x^14/y^3\r<BR>\n" );
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document.write( "Solve<BR>\n" );
document.write( "The square root of 5x+29 = x+3\r<BR>\n" );
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document.write( "I am completely lost when working with roots. Any help would be greatly appreciated! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #217510 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=217510\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> multiply then simplify by factoring.<BR>\n" );
document.write( "Use this as a cube root <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3sqrt%28n%29 ALIGN=MIDDLE  ALT=\"3sqrt%28n%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > symbol<BR>\n" );
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document.write( "(3rd root)of y^7 * (3rd root) of 16y^8<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3sqrt%28y%5E7%29+%2A+3sqrt%2816y%5E8%29 ALIGN=MIDDLE  ALT=\"3sqrt%28y%5E7%29+%2A+3sqrt%2816y%5E8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "We can combine these under single radical<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3sqrt%2816y%5E8y%5E7%29 ALIGN=MIDDLE  ALT=\"3sqrt%2816y%5E8y%5E7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "Add exponents when you multiply<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3sqrt%2816y%5E15%29 ALIGN=MIDDLE  ALT=\"3sqrt%2816y%5E15%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Factor to reveal perfect cubes<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3sqrt%288%2A2%2Ay%5E3%2Ay%5E3%2Ay%5E3%2Ay%5E3%2Ay%5E3%29 ALIGN=MIDDLE  ALT=\"3sqrt%288%2A2%2Ay%5E3%2Ay%5E3%2Ay%5E3%2Ay%5E3%2Ay%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Extract those perfect cubes<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Ay%5E5%2A3sqrt%282%29 ALIGN=MIDDLE  ALT=\"2%2Ay%5E5%2A3sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Use Rational exponents to simplify the third root of x^6<BR>\n" );
document.write( "to raise on power to another power, multiply exponents<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E6%29%5E%281%2F3%29 ALIGN=MIDDLE  ALT=\"%28x%5E6%29%5E%281%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E%286%2A%281%2F3%29%29 ALIGN=MIDDLE  ALT=\"x%5E%286%2A%281%2F3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Find the 16th root of (-8)^16<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28-8%29%5E16%29%5E%281%2F16%29 ALIGN=MIDDLE  ALT=\"%28%28-8%29%5E16%29%5E%281%2F16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-8%29%5E%2816%2A%281%2F16%29%29 ALIGN=MIDDLE  ALT=\"%28-8%29%5E%2816%2A%281%2F16%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-8%29%5E1 ALIGN=MIDDLE  ALT=\"%28-8%29%5E1\"   DISABLED_style= \"max-width:90%; height:auto;\" > = -8<BR>\n" );
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document.write( "Rewrite the 4th root of 23 with a rational exponent.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=23%5E%281%2F4%29 ALIGN=MIDDLE  ALT=\"23%5E%281%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Simplify the 3rd root of -1/64<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3sqrt%28-1%2F64%29 ALIGN=MIDDLE  ALT=\"3sqrt%28-1%2F64%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3sqrt%28%28-1%2F4%29%2A%28-1%2F4%29%2A%28-1%2F4%29%29 ALIGN=MIDDLE  ALT=\"3sqrt%28%28-1%2F4%29%2A%28-1%2F4%29%2A%28-1%2F4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%2F4%29 ALIGN=MIDDLE  ALT=\"%28-1%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Simplify by taking roots of the numerator and denominator<BR>\n" );
document.write( "(3rd root) of 1000x^14/y^3<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3sqrt%281000x%5E14%2Fy%5E3%29 ALIGN=MIDDLE  ALT=\"3sqrt%281000x%5E14%2Fy%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Extract cube root 1/y^3<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2Fy%29%2A3sqrt%281000x%5E14%29 ALIGN=MIDDLE  ALT=\"%281%2Fy%29%2A3sqrt%281000x%5E14%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Extract the cube root of 1000<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810%2Fy%29%2A3sqrt%28x%5E14%29 ALIGN=MIDDLE  ALT=\"%2810%2Fy%29%2A3sqrt%28x%5E14%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Factor inside the radical<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810%2Fy%29%2A3sqrt%28x%5E3%2Ax%5E3%2Ax%5E3%2Ax%5E3%2Ax%5E2%29 ALIGN=MIDDLE  ALT=\"%2810%2Fy%29%2A3sqrt%28x%5E3%2Ax%5E3%2Ax%5E3%2Ax%5E3%2Ax%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Extract<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810%2Fy%29%2Ax%5E4%2A3sqrt%28x%5E2%29 ALIGN=MIDDLE  ALT=\"%2810%2Fy%29%2Ax%5E4%2A3sqrt%28x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( ";<BR>\n" );
document.write( "Solve<BR>\n" );
document.write( "The square root of 5x+29 = x+3 <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%285x%2B29%29+=+x%2B3 ALIGN=MIDDLE  ALT=\"sqrt%285x%2B29%29+=+x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "square both sides:<BR>\n" );
document.write( "5x + 29 = (x+3)^2<BR>\n" );
document.write( "FOIL the right side<BR>\n" );
document.write( "5x + 29 = x^2 + 6x + 9<BR>\n" );
document.write( "combine like terms on the right<BR>\n" );
document.write( "0 = x^2 + 6x - 5x + 9 - 29<BR>\n" );
document.write( "A quadratic equation<BR>\n" );
document.write( "x^2 + x - 20 = 0<BR>\n" );
document.write( "Factors to<BR>\n" );
document.write( "(x+5)(x-4) = 0<BR>\n" );
document.write( "two solutions<BR>\n" );
document.write( "x = -5<BR>\n" );
document.write( "and<BR>\n" );
document.write( "x = +4<BR>\n" );
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document.write( "Check both solution in original equation<BR>\n" );
document.write( "x = -5<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%285%29-5%29%2B29%29+=+-5%2B3 ALIGN=MIDDLE  ALT=\"sqrt%285%29-5%29%2B29%29+=+-5%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28-25%2B29%29+=+-2 ALIGN=MIDDLE  ALT=\"sqrt%28-25%2B29%29+=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%284%29+=+-2 ALIGN=MIDDLE  ALT=\"sqrt%284%29+=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > not a solution<BR>\n" );
document.write( "x = 4<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%285%284%29%2B29%29+=+4%2B3 ALIGN=MIDDLE  ALT=\"sqrt%285%284%29%2B29%29+=+4%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2820%2B29%29+=+7 ALIGN=MIDDLE  ALT=\"sqrt%2820%2B29%29+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2849%29+=+7 ALIGN=MIDDLE  ALT=\"sqrt%2849%29+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" >; a good solution (x=4) </SPAN>\n" );
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