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 Answer:
Question 1: What is square root of negative 4 times square root of negative 9? That is,
find √-4 × √-9
Answer:
√-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.
Have You These Square Roots?
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.