The i means the answer is an imaginary number, because i=−1i=\sqrt{-1}i=−1​. So −144=144−1=12i\sqrt{-144}=\sqrt{144}\sqrt{-1}=12i−144​=144​−1​=12i.

Why it appears

A real number squared can’t be negative, so square roots of negative numbers use the imaginary unit iii. In this case, 144=12\sqrt{144}=12144​=12, and the negative sign contributes the iii.

What to remember

  • −1=i\sqrt{-1}=i−1​=i.
  • −144=12i\sqrt{-144}=12i−144​=12i.
  • The iii tells you the result is not a real number.