The square root of -144 involves imaginary numbers because the square root of a negative number is not defined in the set of real numbers. In mathematics, the square root of a negative number is expressed as a multiple of i, where i is the imaginary unit, defined by i² = -1.

So,

$\sqrt{-144} = \sqrt{144} \times \sqrt{-1} = 12i$

Thus, the square root of -144 is 12i.

Would you like further details on complex numbers or any other related topics?

Here are some related questions for you to explore:

1. How is the imaginary unit i defined and used in complex numbers?
2. What is the difference between real and complex numbers?
3. How do you perform operations (addition, subtraction, etc.) with complex numbers?
4. What is the polar form of a complex number and how is it used?
5. What is the significance of i in engineering or physics?

Tip: When dealing with square roots of negative numbers, always remember that the result will include i, which is a fundamental concept in complex number theory!