What is the Square Root of a Negative Number?

In mathematics, the concept of square roots for negative numbers leads to the field of complex numbers. The square root of a negative number cannot be a real number, as no real number squared gives a negative result. This is where the imaginary unit ‘i’ comes into play, defined as the square root of -1.

Answer: The square root of a negative number is an imaginary number, represented as a multiple of the imaginary unit ‘i’.

For example, consider finding the square root of -4. This can be expressed as:

√−4= √4 ×−1 = 2i

Here, √4​ is 2, and √−1​ is defined as ‘i’. Therefore, the square root of -4 is written as 2i.

Hence, the Square Root of a Negative Number is represented by an imaginary number.

This concept is crucial in advanced mathematics, particularly in fields like engineering, physics, and complex analysis. Imaginary and complex numbers allow for solutions to equations that would otherwise have no solution in the real number system, thereby expanding the scope of mathematical and scientific problem-solving.