# Square Root of Negative 4 Explained

The square root of negative 4 is equal to 2i, where i=√-1 is the imaginary complex number. Note that the square roots of -4 are the solutions of the quadratic equation x2+4=0, that is, x2=-4. In this post, we will learn how to find the square root of -4.

## What is the Square root of -4

Answer: The square root of -4 is 2i, that is, √-4 =2i.

Solution:

Note that -4 can be written as follows:

-4 = 4 × -1 …(∗)

Now to find the square root of -4, we need to take the square root on both sides of (∗), doing so we will get that

$\sqrt{-4}=\sqrt{4 \times (-1)}$

= $\sqrt{4} \times \sqrt{-1}$. Here we have used the square root multiplication rule: √(m×n) = √m × √n.

= 2 × √-1, as the square root of 4 is 2.

= 2i where i=√-1.

So the square root of negative 4 is 2i.

We know that if x is a square root, then -x is also a square root. Therefore, we can obtain that

√-4 =2i, -2i.

Video Solution:

Question 1: What is square root of negative 4 times square root of negative 9? That is,

find √-4 × √-9

√-4 × √-9

= 2i × 3i

= 6i2

= -6 as i2=-1.

So the product of the square root of negative 4 and the square root of negative 9 is equal to -6.

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## FAQs

### Q1: What is square root of -4?

Answer: The square root of -4 is 2i, where i=√-1.

### Q2: Is square root of negative 4 an integer?

Answer: As √-4 =2i, square root of negative 4 is not an integer, it is an imaginary complex number.