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Square Root

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

Written by Prerit Jain

Updated on: 12 Aug 2023

### 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.

## 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 = 132
Hence, 169 = 13

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?
1211/2 or 1210.5 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 is √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

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Prerit Jain

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