Question 184754
Jane comes up to you with the following dilemma: 
She read in the book that {{{i^2 = -1}}} but she 
did some math on her own and came up with the following: 
{{{i^2=i*i=sqrt(-1)sqrt(-1)=sqrt((-1)(-1))=sqrt((-1)^2)=sqrt(1)=1}}} 
Her question is how can this be? Write a paragraph explaining how to resolve this dilemma for her.
<pre><font size = 4 color ="indigo"><b>
The violation of rules for multiplying under
radicals is violated in this step above:

{{{sqrt(-1)sqrt(-1)=sqrt((-1)(-1))}}}

That is incorrect.

When multiplying two square roots, we can
only multiply POSITIVE numbers under square
root radicals, NEVER negative numbers. 
If a negative number is under a square root
radical such as {{{sqrt(-7)}}}, we must first 
write it as {{{i*sqrt(7)}}} so that there will 
only be a positive number under the square root
radical.  And we simply learn that {{{i^2=i*i=-1}}} 
by definition.

Edwin</pre>