Can you help me with this math problem by giving me a step-by-step solution? here it is below:

Evaluate the expression, or state that the expression is not a real number.
squareroot -36

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. The expression is a real number. - 36 = blank (Simplify your answer.)

B. The expression is not a real number.

1 answer

The expression you provided is \(\sqrt{-36}\).

Step 1: Understanding Square Roots

The square root of a number \(x\) is a value \(y\) such that \(y^2 = x\). This means that for a square root to be a real number, \(x\) must be greater than or equal to zero.

Step 2: Analyzing the Given Expression

In this case, you have \(\sqrt{-36}\). Since \(-36\) is less than zero, it does not have a real square root.

Step 3: Using Imaginary Numbers

However, in mathematics, the square root of a negative number can be expressed using imaginary numbers. The square root of \(-1\) is denoted as \(i\). Therefore:

\[ \sqrt{-36} = \sqrt{-1 \cdot 36} = \sqrt{-1} \cdot \sqrt{36} = i \cdot 6 = 6i \]

Conclusion

Since \(\sqrt{-36}\) results in an imaginary number (not a real number), the correct response is:

B. The expression is not a real number.