<PRE><B>Question 1133226</B>
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{{{sqrt(-80) = sqrt(-1)*sqrt(80) = i*sqrt(80) = i*sqrt(16*5) = i*sqrt(16)*sqrt(5) = 4i*sqrt(5)}}}&lt;br&gt;
Answer d.&lt;br&gt;
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).&lt;br&gt;
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Added after reading the response by tutor @ikleyn....&lt;br&gt;
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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).&lt;br&gt;
But when you write the number sqrt(4), or sqrt(-80), for use in a calculation, it has to have a single value.&lt;br&gt;
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.&lt;br&gt;
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.
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