Problem 5 - College Algebra

Question

Evaluate each expression or indicate that the root is not a real number. $$\sqrt{-36}$$

Step-by-Step Solution

Answer

The square root of \(-36\) is not a real number. However, in the complex number system, it is \(6i\).

Step 1: Identify the Type of Number

Identify the given number as negative. In this case, it is -36.

Step 2: Try to Evaluate the Square Root

Attempt to calculate the square root of the number. But since the given number is negative, its square root cannot be calculated using the standard method because a negative number does not have a real square root.

Step 3: State the Result

The square root of \(-36\) does not exist in the real number system. It's a complex number, and if we allow for complex numbers, the square root of \(-36\) would be \(6i\) where \(i\) is the imaginary unit.