# Square Root of -1

The square root of -1 is the number, which multiplied by itself 2 times, is -1. In other words, this number to the power of 2 equals -1.

Besides the complex values of \sqrt[2]{-1} along with an explanation, on this page you can also find what the elements of the square root of -1 are called.

In addition to the terminology, we have a calculator you don’t want to miss:

## Square Root Calculator

\sqrt[2]{-1} = \pm1iIf you have been looking for the square root of negative one, then you are right here, too.

The term can be written as \sqrt[2]{-1} \hspace{3 mm}or\hspace{3 mm} -1^{1/2}.

As the index 2 is even and -1 is less than 0, -1 has two complex square roots \in \mathbb{C}:

\sqrt[2]{-1}, which is positive and called principal square root of -1, and −\sqrt[2]{-1}, which is negative.

Together, they are denominated as ±\sqrt[2]{-1}.

Although the principal negative square root of negative one is only one of the two square roots, the term “square root of -1” usually refers to the positive number.

Make sure to understand that -1 has no real square roots \in \mathbb{R}!

Next, we have a look at the inverse function.

### Inverse of Square Root of -1

Extracting the square root is the inverse operation of ^2:\underbrace{ {\rm \sqrt[2]{-1} \times\thinspace ... \times\thinspace \sqrt[2]{-1}} }_{\rm 2 \thickspace times} = \sqrt[2]{-1}^{2}= -1In the following paragraph, we are going to name the elements of this √.

## What is the Square Root of -1?

You already have the answer to that question, and you also know about the inverse operation of -1 square root.

Keep reading to learn what the parts are called.

• \sqrt[2]{-1} is the square root of -1 symbol
• 2 is the index
• -1 = radicand; the radicand is the number below the radical sign
• Square root = ±1i
• √ is called radical symbol or radical only

Second root of -1 = ±1i

As a sidenote: All values on this page have been rounded to ten decimal places.

Now you really know all about \sqrt[2]{-1}, including its values, parts and the inverse.

If you need to extract the 2nd root of any other real or complex number use our calculator above.

Simply insert the number of which you want to find the square root (e.g. -1); the calculation is done automatically.

If you like our information about \sqrt[2]{-1}, then a similar square root you may be interested in is, for example: square root of negative 3.

In the following table you can find some imaginary square roots

## Table

The aim of this table is to provide you with an overview of the complex square roots close to -1.
-5\sqrt[2]{-5}±2.2360679775i
-4\sqrt[2]{-4}±2i
-3\sqrt[2]{-3}±1.7320508076i
-2\sqrt[2]{-2}±1.4142135624i
-1\sqrt[2]{-1}±1i
0\sqrt[2]{0}±0i
1\sqrt[2]{1}±1i
2\sqrt[2]{2}±1.4142135624i
3\sqrt[2]{3}±1.7320508076i
A few lines down from here we review the FAQs.

## Square Root of Negative One

If you have been searching for what's the square root of negative one or 2nd root of -1, then you are reading the right post as well.

The same is true if you typed 2 root of -1 or -1 2 root in the search engine of your preference, just to name a few similar terms.

Right below you can find the frequently asked questions in the context.

### FAQs About the Square Root of -1

How Many Real Square Roots Does -1 Have?

-1 has no real square roots, because the radicand -1 is negative. However, -1 does have the two complex square roots ±1i.

What to the Second Power Equals -1?

The square root of -1 to the power of 2 equals -1.

How Do You Find the Square Root of -1?

Start with an initial guess such that 2 times that value equals approximately 1, then keep improving the guess until you have the required precision. Prepend ± to the value and append “i”.

What is -1 to the Square Root?

-1 to the square root = -1^1/2 = ±1i.

What Number is the Square Root of -1?

The square root of -1 = ±1i.

How Do You Solve the Square Root of -1?

To compute the 2nd root of 1 use a calculator, and/or employ the Newton–Raphson method. Append “i”.

What is the Value of 2 Root -1?

The value of 2 root -1 is ±1i.

Ahead is the wrap-up of our information.

## Summary

To sum up, the complex square roots of -1 are ±1i.

Finding the second root of the number -1 is the inverse operation of rising the \sqrt[2]{-1} to the power of 2. That is to say, (±1i)2 = -1.

Note that you can also locate roots like \sqrt[2]{-1} by means of the search form in the menu and in the sidebar of this site.

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Posted in Square Roots