Square Root of a Negative Number

In mathematics, square root of a number means a number multiplied by itself. Numbers multiplied by themselves belong to a special class called roots. These numbers include 2 times 2, 3 times 3, 4 and 4 etc. That said, a square of a number has two square root that is positive and negative value. Moreover, negative numbers have no real square root. This is because a square is always positive or 0. Suppose the square root of an integer is an integer, this means the square is perfect. Let’s explore and understand the square root of negative number.

What is a negative square root?

In most cases, when someone asks for a square root, they think of a positive value. Therefore, it is referred to as the principle square root. Nonetheless, square root can also be negative. For example, -5 can be a square root of 25, -6 can be a square root of 36.  Therefore, the negative square root is similar to the principle square root but in a negative version.

How to find Square root of a Negative number

Step 1: Ignore the negative sign and find the square root

Step 2: Multiply the answer by i (iota)

Examples

1. What is the square root of -144?

Solution

Step 1: The square root of 144 is 12

Step 2: Multiply 12 by iota

Therefore the square root of -144 is

=12 i

2. What is the square root of 900?

Solution

Step 1: The square root of 900 is 30

Step 2: Multiply 30 by an imaginary number iota

Therefore the square root of -900 is

                = 30 i

3. Find the square root of negative 400

Solution

Step 1: The square root of 400 is 20

Step 2: Multiply 20 by an imaginary number iota

Therefore the square root of negative 400 is

=20