The square root of negative 9 is equal to 3i. Here i=√-1 is an imaginary complex number. The square roots of -9 are the solutions of the quadratic equation x^{2}+9=0. In this post, we will learn how to find the square root of -9.

## What is the Square root of -9

**Answer:** The square root of -9 is 3i, that is, √-9 =3i.

**Solution:**

Note that 9 is a perfect square, which is a square root 3. First, we write -9 as follows:

-9 = 9 × -1 **…(∗)**

Taking square roots on both sides of **(∗)** to get the value of root -9. Thus,

$\sqrt{-9}=\sqrt{9 \times (-1)}$

= $\sqrt{9} \times \sqrt{-1}$, by the surd rule: √(m×n) = √m × √n.

= 3 × √-1, as we know the square root of 9 is 3.

= 3i where i=√-1 is a complex number.

**Hence the square root of negative 9 is 3i.**

**Note**: If x is a square root, then -x is also a square root. Therefore, the square root of negative 9 are given by

√-9 =3i, -3i.

Video Solution:

Question Answer:

**Question 1:** Is square root of negative 9 a real number?

**Answer:**

We know that the square root of 9 is equal to either 3i or -3i. As i is a complex number, both 3i and -3i is also complex. So the square root of negative 9 cannot be a real number.

Square root of negative 9 is a complex number.

Have You These Square Roots?

## FAQs

### Q1: What is square root of -9?

Answer: The square root of -9 is 3i, where i=√-1 is a complex number.

### Q2: Is square root of negative 9 an integer?

Answer: Note that √-9 =3i. So square root of negative 9 cannot be an integer. Square root of -9 is an imaginary complex number.