document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=29360>Question 29360</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Someone please help me by Solving Equations With Radicals, thanks!\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #16168 by </B><A HREF=/tutors/aboutme.mpl?userid=sdmmadam@yahoo.com><B>sdmmadam@yahoo.com(530)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=sdmmadam@yahoo.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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=16168\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1.sqrt(x-2) = 4<BR>\n" );
document.write( "Squaring both the sides<BR>\n" );
document.write( "(x-2) =4^2    (using [sqrt(p)]^2 = p and here p = (x-2) )<BR>\n" );
document.write( "x-2 = 16<BR>\n" );
document.write( "x = 16+2<BR>\n" );
document.write( "x=18<BR>\n" );
document.write( "Answer: x= 18<BR>\n" );
document.write( "Verification:sqrt(x-2) =sqrt(18-2)= sqrt(16) = 4 which is what is given.\r<BR>\n" );
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document.write( "2.   2[sqrt(x+3)] = 10<BR>\n" );
document.write( "Squaring both the sides,<BR>\n" );
document.write( "4(x+3) =10^2     (using [sqrt(p)]^2 = p and here p = (x+3) )<BR>\n" );
document.write( "4x+12 = 100<BR>\n" );
document.write( "4x= 100-12<BR>\n" );
document.write( "4x=88<BR>\n" );
document.write( "x=88/4=22<BR>\n" );
document.write( "Answer: x=22<BR>\n" );
document.write( "Verification:<BR>\n" );
document.write( "2[sqrt(x+3)] =22[sqrt(22+3)]=2[sqrt(25)] =2X(5) = 10 which is correct \r<BR>\n" );
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document.write( "3. x = sqrt(x+6)<BR>\n" );
document.write( "Squaring both the sides,<BR>\n" );
document.write( "x^2 = (x+6)     (using [sqrt(p)]^2 = p and here p = (x+6) )<BR>\n" );
document.write( "x^2-x-6=0 ----(*)Which is a quadratic in x<BR>\n" );
document.write( "x^2-3x+2x-6 =0 <BR>\n" );
document.write( "(x^2-3x)+(2x-6) =0 (by additive associativity)<BR>\n" );
document.write( "x(x-3)+2(x-3)<BR>\n" );
document.write( "(x-3)(x+2)= 0<BR>\n" );
document.write( "(x-3) =0 implies x=3 and <BR>\n" );
document.write( "(x+2)= 0 implies x= -2<BR>\n" );
document.write( "Answer: x=3 and x=-2<BR>\n" );
document.write( "Verification: We may verify orally and see that both the values hold.<BR>\n" );
document.write( "Note:(On the LHS of (*) splitting the middle term two terms <BR>\n" );
document.write( "whose sum is the mid term and whose product is the product of the <BR>\n" );
document.write( "square term and the constant term. <BR>\n" );
document.write( "So here (-x) = (-3x+2x) and (-3x)X(2x) = -6x^2 = (x^2)X(-6)\r<BR>\n" );
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document.write( "4. sqrt(x) + 1 = 5<BR>\n" );
document.write( "sqrt(x) = 5 - 1<BR>\n" );
document.write( "sqrt(x) =4<BR>\n" );
document.write( "Squaring both the sides<BR>\n" );
document.write( "x= 16     (using [sqrt(p)]^2 = p and here p = (x) )<BR>\n" );
document.write( "Answer: x=16<BR>\n" );
document.write( "Verification: Very clear orally even!\r<BR>\n" );
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