Problem 6 - College Algebra

Question

Evaluate each expression or indicate that the root is not a real number. $$\sqrt{-25}$$

Step-by-Step Solution

Answer

The square root of -25 is \(5i\)

Step 1: Understanding Imaginary Numbers

In the context of mathematics, the square root of a negative number does not result in a real number. Instead, it results in an imaginary number. The unit of imaginary numbers is \(i\), where \(i^2 = -1\). Therefore, \(\sqrt{-1} = i \).

Step 2: Applying the Imaginary Number Rule

We can treat the -25 as -1 multiplied by 25, so \(\sqrt{-25} = \sqrt{-1*25}\). According to the rules of square roots,\(\sqrt{-1*25} = \sqrt{-1} * \sqrt{25}\). Applying the imaginary unit rule, \(\sqrt{-1}\) is \(i\), and \(\sqrt{25}\) is 5.

Step 3: Final Answer

So, the square root of -25 is \(5i\)