Square Root

# What Is the Square Root of -1? | Does -1 Have a Square Root?

Written by Prerit Jain

Updated on: 12 Aug 2023

Contents

### What Is the Square Root of -1? | Does -1 Have a Square Root?

The square root of -1 is i. The square root of any number has two possibilities which are a positive and a negative number. Let us take the number 36 as an example. The √36 = 6. The negative integer number or digit is not considered a square number and only the positive roots are used. That is because when we square or multiply those negative digits we again get a positive number.

That is (-6) (-6) = 36. Therefore the negative square of any number is considered imaginary and not a real value. This rule applies to -1. When we multiply (-1) (-1) we get 1. The thumb rule for finding the square root of any number is when you multiply a number twice it should give the original value but here we get 1 and not -1. Thus the imaginary roots of -1 are represented as i.

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**Solved examples**

**Q1: Find the square root of -9**

A1: √9 =√9 -1

Hence the square root of -9=3 i

**Q2: Sonu has to find the square root of 36 using the long division method, help him**

A2: √**36 = 6**

**Q3: Find the square root of 1.**

A3: The √1 = 1

**Q4: Find the square root of -100.**

A4: The √100 ×-1

√100 = 10

Hence, the √100 = 10i

**Q5: What is the square root of 169?**

A5:169 = 13 × 13**√**169 = 13^{2}

Hence, **√**169 = 13

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**Frequently asked questions**

**What is the √-1**

√-1 = i

**Which method is used to find the -1**

You can’t find the actual square root of the number as they have only imaginary roots and not real roots.

**How to write the square root of 121 in exponential form?**

121^{1/2 }or 121^{0.5 }is the exponential way to write √121

**How to write the square root of 81 in radical form?**

The radical form of writing square root i**s √**81

**What are the methods to find the square root of a number?**

There are three methods to find the square root of a number

Prime factorization method

Long division method

Repeated subtraction

Written by

Prerit Jain