What Is the Square Root of Negative One?

By Staff WriterLast Updated Mar 25, 2020 12:07:42 PM ET

The square root of negative one is "i," the imaginary number. This concept is immensely useful in mathematics, as it allows for there to be square roots of negative numbers, which is otherwise not possible using only real numbers.


Any number that includes a negative square root is called an imaginary number. For example, the square root of -9 equals 3i, an imaginary number. When an imaginary number and a real number are combined, for example 2 + 3i, this is called a complex number. Complex numbers have many real world applications, including manipulating sound waves and calculating electrical currents.