Evaluate square root of -25

Problem

$\sqrt{-25}$

Solution

1. Identify the expression as the square root of a negative number, which requires the use of the imaginary unit $i$ where $i=\sqrt{-1}$

2. Rewrite the radicand as a product of a positive number and $-1$

$\sqrt{-25}=\sqrt{25\cdot (-1)}$

3. Apply the product property of radicals, $\sqrt{a\cdot b}=\sqrt{a}\cdot \sqrt{b}$

$\sqrt{25\cdot (-1)}=\sqrt{25}\cdot \sqrt{-1}$

4. Simplify the square root of the positive constant and substitute $i$ for $\sqrt{-1}$

$\sqrt{25}\cdot \sqrt{-1}=5i$

Final Answer

$\sqrt{-25}=5i$

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