Why can't the square root of a negative number be found? How do mathematicians deal with this when it is not possible technically?

Expert Answers
justaguide eNotes educator| Certified Educator

The square root of a number A is another number B such that `B^2 = B xx B = A`

If A were a negative number, there is no real value of B for which `B^2 = A` . This is due to the fact that the product of two negative numbers and the product of two positive numbers gives a result that has a positive sign.

In spite of this there are many occasions that arise when mathematical problems are being solved that require the value of the square root of a negative number.

This has been facilitated by the creation of complex numbers. The notation i denotes the square root of -1. `i^2 = -1` . Using complex numbers the absence of a real number that is the square root of a negative number is dealt with.