document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=422841>Question 422841</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I do not fully understand radical expressions like 7 times the square root of 12. How exactly do you find the answer and is there a good way for me to check my answer on paper or with a calculator? \r<BR>\n" );
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document.write( "Also how do you add and subtract them to get answers with a number outside a square root like 6 times the square root of 54 or something. \r<BR>\n" );
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document.write( "One more question. When there are letters and numbers with the variable is it any different to solve. For example the square root of 128n^17  \r<BR>\n" );
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document.write( "Help would be much appreciated! Im trying to learn all this without a teacher. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #295084 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=295084\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I do not fully understand radical expressions like 7 times the square root of 12.<BR>\n" );
document.write( "Taking your example <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7sqrt%2812%29 ALIGN=MIDDLE  ALT=\"7sqrt%2812%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Factor 12 in a way the reveals at perfect square<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7sqrt%284%2A3%29 ALIGN=MIDDLE  ALT=\"7sqrt%284%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Extract the square root of 4, which is 2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2A2sqrt%283%29 ALIGN=MIDDLE  ALT=\"7%2A2sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14sqrt%283%29 ALIGN=MIDDLE  ALT=\"14sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, no further action can be taken<BR>\n" );
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document.write( "Check this on a calc: enter 7*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2812%29 ALIGN=MIDDLE  ALT=\"sqrt%2812%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get 24.2487..<BR>\n" );
document.write( "Then enter your solution: 14*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%29 ALIGN=MIDDLE  ALT=\"sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get 24.2487.., the same if you did it right.<BR>\n" );
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document.write( "Also how do you add and subtract them to get answers with a number outside a square root like 6 times the square root of 54 or something.<BR>\n" );
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document.write( "You can add and subtract only like terms,  For example <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3sqrt%282%29 ALIGN=MIDDLE  ALT=\"3sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sqrt%282%29 ALIGN=MIDDLE  ALT=\"2sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5sqrt%282%29 ALIGN=MIDDLE  ALT=\"5sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "but <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3sqrt%282%29 ALIGN=MIDDLE  ALT=\"3sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sqrt%283%29 ALIGN=MIDDLE  ALT=\"2sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > are not like terms and can't be added<BR>\n" );
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document.write( "However, after simplifying they may be like terms, this example<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sqrt%286%29 ALIGN=MIDDLE  ALT=\"2sqrt%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6sqrt%2854%29 ALIGN=MIDDLE  ALT=\"6sqrt%2854%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Factor 54 to reveal a perfect square<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sqrt%286%29 ALIGN=MIDDLE  ALT=\"2sqrt%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6sqrt%289%2A6%29 ALIGN=MIDDLE  ALT=\"6sqrt%289%2A6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Extract the square root of 9<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sqrt%286%29 ALIGN=MIDDLE  ALT=\"2sqrt%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2A3sqrt%286%29 ALIGN=MIDDLE  ALT=\"6%2A3sqrt%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sqrt%286%29 ALIGN=MIDDLE  ALT=\"2sqrt%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18sqrt%286%29 ALIGN=MIDDLE  ALT=\"18sqrt%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > =<BR>\n" );
document.write( "now they are like terms so we have: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20sqrt%286%29 ALIGN=MIDDLE  ALT=\"20sqrt%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( ":<BR>\n" );
document.write( "One more question. When there are letters and numbers with the variable is it any different to solve. For example the square root of 128n^17 <BR>\n" );
document.write( ":<BR>\n" );
document.write( "Using <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28128n%5E17%29 ALIGN=MIDDLE  ALT=\"sqrt%28128n%5E17%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > we can factor to reveal perfect squares<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2864%2A2%2An%5E16%2An%29 ALIGN=MIDDLE  ALT=\"sqrt%2864%2A2%2An%5E16%2An%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "remember the sqrt of n^16 is n^8 (n^8*n^8), so we have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2An%5E8%2Asqrt%282n%29 ALIGN=MIDDLE  ALT=\"8%2An%5E8%2Asqrt%282n%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "We treat variables the same way, just remember the law of exponents. </SPAN>\n" );
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