document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=118059>Question 118059</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use property 1 to simplify each of the radical expressions. Assume that all variables represent positive real numbers.\r<BR>\n" );
document.write( "\n" );
document.write( "1. square root of 50\r<BR>\n" );
document.write( "\n" );
document.write( "2. square root of 72x cubed  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #86140 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=86140\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> #1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2850%29 ALIGN=MIDDLE  ALT=\"sqrt%2850%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The goal of simplifying expressions with square roots is to factor the radicand into a product of two numbers. One of these two numbers must be a perfect square. When you take the square root of this perfect square, you will get a rational number.\r<BR>\n" );
document.write( "\n" );
document.write( "So let's list the factors of 50\r<BR>\n" );
document.write( "\n" );
document.write( "Factors:\r<BR>\n" );
document.write( "\n" );
document.write( "1, 2, 5, 10, 25, 50\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Notice how 25 is the largest perfect square, so lets factor 50 into 25*2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2825%2A2%29 ALIGN=MIDDLE  ALT=\"sqrt%2825%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor 50 into 25*2<BR>\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2825%29%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"sqrt%2825%29%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the square roots using the identity <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"5%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of the perfect square 25 to get 5 <BR>\n" );
document.write( " <BR>\n" );
document.write( "So the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2850%29 ALIGN=MIDDLE  ALT=\"sqrt%2850%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"5%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "----------------------------<BR>\n" );
document.write( "Check:\r<BR>\n" );
document.write( "\n" );
document.write( "Notice if we evaluate the square root of 50 with a calculator we get\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2850%29=7.07106781186548 ALIGN=MIDDLE  ALT=\"sqrt%2850%29=7.07106781186548\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "and if we evaluate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"5%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > we get\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2Asqrt%282%29=7.07106781186548 ALIGN=MIDDLE  ALT=\"5%2Asqrt%282%29=7.07106781186548\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This shows that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2850%29=5%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"sqrt%2850%29=5%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So this verifies our answer \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<hr>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "#2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2872%2Ax%5E3%29 ALIGN=MIDDLE  ALT=\"sqrt%2872%2Ax%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2836%2A2%2Ax%5E3%29 ALIGN=MIDDLE  ALT=\"sqrt%2836%2A2%2Ax%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=72 ALIGN=MIDDLE  ALT=\"72\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36%2A2 ALIGN=MIDDLE  ALT=\"36%2A2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2836%2A2%2Ax%2Ax%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%2836%2A2%2Ax%2Ax%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <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;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Ax%5E2 ALIGN=MIDDLE  ALT=\"x%2Ax%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2836%29%2Asqrt%282%29%2Asqrt%28x%29%2Asqrt%28x%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%2836%29%2Asqrt%282%29%2Asqrt%28x%29%2Asqrt%28x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the square root using the identity <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Asqrt%282%29%2Asqrt%28x%29%2Asqrt%28x%5E2%29 ALIGN=MIDDLE  ALT=\"6%2Asqrt%282%29%2Asqrt%28x%29%2Asqrt%28x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of the perfect square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36 ALIGN=MIDDLE  ALT=\"36\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get 6 <BR>\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Asqrt%282%29%2Asqrt%28x%29%2Ax ALIGN=MIDDLE  ALT=\"6%2Asqrt%282%29%2Asqrt%28x%29%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of the perfect squares <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;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( " \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Ax%2Asqrt%28x%29%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"6%2Ax%2Asqrt%28x%29%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the terms \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Ax%2Asqrt%282x%29 ALIGN=MIDDLE  ALT=\"6%2Ax%2Asqrt%282x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Group the square root terms \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2872%2Ax%5E3%29 ALIGN=MIDDLE  ALT=\"sqrt%2872%2Ax%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Ax%2Asqrt%282x%29 ALIGN=MIDDLE  ALT=\"6%2Ax%2Asqrt%282x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );