document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1133226>Question 1133226</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what is the correct solution?\r<BR>\n" );
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document.write( "√-80 (square root of -80)\r<BR>\n" );
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document.write( "a.i√-80<BR>\n" );
document.write( "b.-4i√5<BR>\n" );
document.write( "c.-80i<BR>\n" );
document.write( "d.4i√5\r<BR>\n" );
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document.write( "*√ (symbol of a square root) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #750406 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=750406\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28-80%29+=+sqrt%28-1%29%2Asqrt%2880%29+=+i%2Asqrt%2880%29+=+i%2Asqrt%2816%2A5%29+=+i%2Asqrt%2816%29%2Asqrt%285%29+=+4i%2Asqrt%285%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Answer d.<br><BR>\n" );
document.write( "Note that both answer b and answer d, when squared, give the same result of -80.  However, just as 2 and -2 squared both give the result 4 but sqrt(4) = 2 and not -2, the square root of -80 is 4i*sqrt(5) and not -4i*sqrt(5).<br><BR>\n" );
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document.write( "Added after reading the response by tutor @ikleyn....<br><BR>\n" );
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document.write( "It is true that, in the complex domain, every number, real or complex, has two square roots.  So the square root of 4 has two square roots, 2 and -2; and the square root of -80 has two square roots, 4i*sqrt(5) and -4i*sqrt(5).<br><BR>\n" );
document.write( "But when you write the number sqrt(4), or sqrt(-80), for use in a calculation, it has to have a single value.<br><BR>\n" );
document.write( "A high school student who wrote as an answer on a test that the square root of 4 is -2 would be marked wrong; and if he used -2 as the value of the square root of 4 in a calculation, he would end up with the wrong answer.<br><BR>\n" );
document.write( "In this problem, two of the answer choices are 4i*sqrt(5) and -4i*sqrt(5).  Since it would be presumed that these are answer choices on a test with only one correct answer, the answer should be d only.<BR>\n" );
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