what does the i mean in the answer to the square root of -144
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.