Write as a real number or a product of a real number and i.
-$\sqrt { - 5 } \cdot \sqrt { - 5 }$
A) $2 i \sqrt { - 5 }$
B) $- 5$
C) 5
D) $- 5 \mathrm { i }$

Question

Quizplus · Accepted Answer

The product of two square roots of negative numbers, $\sqrt{-5} \cdot \sqrt{-5}$, simplifies to $\sqrt{(-5) \cdot (-5)} = \sqrt{25} = 5$. However, since both -5 are under square roots and are multiplied, the negative signs cancel out (because $i^2 = -1$), resulting in a positive real number, not 5. The correct simplification should be $(-i\sqrt{5}) \cdot (-i\sqrt{5}) = (-i)^2(\sqrt{5})^2 = 1 \cdot 5 = 5$, indicating an error in my initial explanation. The correct answer is actually -5, considering the properties of imaginary numbers correctly, where the multiplication of two identical square roots of negative numbers results in the positive value of the number under the square root.

Write as a Real Number or a Product of a Real