Square Root of Negative 9

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 x²+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.

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