document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=374416>Question 374416</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Does this look correct? Have I completed all steps? If not can you show me what I am missing. Your help will be much appreciated. Note the \"x\" is for multiplication.\r<BR>\n" );
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document.write( "&#8730;175y^6 <BR>\n" );
document.write( "= &#8730;175×y^2 <BR>\n" );
document.write( "= &#8730;175×y^2<BR>\n" );
document.write( "= &#8730;175×y </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #266615 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=266615\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28175y%5E6+%29 ALIGN=MIDDLE  ALT=\"sqrt%28175y%5E6+%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%28175%2Ay%5E2+%29 ALIGN=MIDDLE  ALT=\"sqrt%28175%2Ay%5E2+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Where did the 6 go??<br><BR>\n" );
document.write( "To simplify a square root (where there are no fractions), like this one, you look for perfect square factors of the radicand. (The expression inside a radical is called the radicand.) Your radicand has a couple of perfect square factors:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2825%2A7%2A%28y%5E3%29%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%2825%2A7%2A%28y%5E3%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Next I like to use the Commutative Property to rearrange the factors so the perfect squares are in front:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2825%2A%28y%5E3%29%5E2%2A7%29 ALIGN=MIDDLE  ALT=\"sqrt%2825%2A%28y%5E3%29%5E2%2A7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Next we use a property of radicals, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%28a%2C+p%2Aq%29+=+root%28a%2C+p%29%2Aroot%28a%2C+q%29 ALIGN=MIDDLE  ALT=\"root%28a%2C+p%2Aq%29+=+root%28a%2C+p%29%2Aroot%28a%2C+q%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, to separate all the perfect square factors into their own square roots:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2825%29%2Asqrt%28%28y%5E3%29%5E2%29%2Asqrt%287%29 ALIGN=MIDDLE  ALT=\"sqrt%2825%29%2Asqrt%28%28y%5E3%29%5E2%29%2Asqrt%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The square roots of the perfect squares can be simplified:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2Ay%5E3%2Asqrt%287%29 ALIGN=MIDDLE  ALT=\"5%2Ay%5E3%2Asqrt%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "One more detail...<BR>\n" );
document.write( "Square roots, including <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28175y%5E6+%29 ALIGN=MIDDLE  ALT=\"sqrt%28175y%5E6+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, are supposed to be positive (or zero). Our simplified expression should also be positive (or zero), too. However,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2Ay%5E3%2Asqrt%287%29 ALIGN=MIDDLE  ALT=\"5%2Ay%5E3%2Asqrt%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "could be negative if y is negative. Since we do not know that y cannot be negative, then we must use absolute value to ensure a positive (or zero) expression:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2Aabs%28y%5E3%29%2Asqrt%287%29 ALIGN=MIDDLE  ALT=\"5%2Aabs%28y%5E3%29%2Asqrt%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2 ALIGN=MIDDLE  ALT=\"y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > cannot be negative this can also be written as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2Ay%5E2%2Aabs%28y%29%2Asqrt%287%29 ALIGN=MIDDLE  ALT=\"5%2Ay%5E2%2Aabs%28y%29%2Asqrt%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Either of these last two is your simplified expression. </SPAN>\n" );
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