**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 **

**Square Root of a negative number video tutorial**

**Other Solved Examples**

What is the Square Root of -70?

What is the Square Root of -390?

What is the Square Root of -286?

What is the Square Root of -97?

What is the Square Root of -500?

**Frequently Asked Questions**

**Can square root be negative?**

Even though most of the times, we often assume square roots are only positive, square root can also be negative. When a negative number is multiplied by a negative number, we get a positive number. For instance, square root of 4 are -2 and 2. You can multiply (-2) × (-2) =4. Similarly, square root of 9 are -3 and 3. Multiply (-3) × (-3) =9.

**Can we square root a negative number**?

Theoretically, there is no way of taking square root of a negative number. When we multiply two negative numbers together, you get a positive number. When calculating square root of a negative number, the negative number can be written as a multiple of -1. For example, -25 is written as -1×25.