To find the real square roots of -4, recall that the square root of a number [tex]\( x \)[/tex] is a value [tex]\( y \)[/tex] such that [tex]\( y^2 = x \)[/tex].
1. Consider the equation for the square root:
[tex]\[ y^2 = -4 \][/tex]
2. For a square root to be real, the value inside the square root must be non-negative (either zero or a positive number). However, here we have [tex]\(-4\)[/tex], which is negative.
3. Since no real number squared gives a negative result, there are no real numbers [tex]\( y \)[/tex] such that [tex]\( y^2 = -4 \)[/tex].
4. Therefore, there are no real square roots of -4.
Based on this reasoning, the answer is:
Answer: [tex]$\square$[/tex]
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