You can square root a negative number with an imaginary number "i".

The story behind the answer

True—within the complex numbers. There’s no real number whose square is negative, so mathematicians define the imaginary unit i with i² = −1. That lets us write square roots of negatives as sqrt(−a) = i·sqrt(a) for any a ≥ 0; for example, sqrt(−9) = 3i.

Imaginary and complex numbers (a + bi) arose in the 16th century while solving cubic equations and now underpin engineering, signal processing, and quantum mechanics. You can picture them on the Argand plane, with the horizontal axis for real parts and the vertical for imaginary parts, and connect them to rotations via Euler’s formula e^{iθ} = cosθ + i sinθ. Memory tip: see a minus under the root? Pull out an i—turn it positive, then multiply by i.