Question

What is the principal square root of -2500?

Answer 1

Answer:The principal square root is the positive number square root. Unless otherwise stated, "the square root" of a number refers ONLY to the principal square root. The square root of n2 is the absolute value of n. When solving a simple equation such as x2 = 25, it must be observed that there are two solutions.

Explanation:

The principal square root is the positive number square root. Unless otherwise stated, "the square root" of a number refers ONLY to the principal square root. The square root of n2 is the absolute value of n. When solving a simple equation such as x2 = 25, it must be observed that there are two solutions.

Answer 2

Real solutions: none

Complex principal solution: 50i

Explanation:

sqrt (-2500)

If we are working with only real numbers, then there is no solution since it is a negative number and negative numbers have to square root in the real domain

If we are in the complex realm

sqrt(-2500) = sqrt(-1) sqrt(2500)

= i (50)

We only took the positive values since we are taking the principal square root

= 50i