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Square Root

What Is the Square Root of 12? | How to Find the Square Root of 12?

Written by Prerit Jain

Updated on: 12 Aug 2023

What Is the Square Root of 12? | How to Find the Square Root of 12?

What Is the Square Root of 12? | How to Find the Square Root of 12?

The square root of 12 is 3.464. The square root of a value is given when a particular number is multiplied by itself and gives the number or a number when they have squared equals to a specified number. The number 6 is a positive real number that when multiplied by itself produces the number. The square root of 6 is mentioned as 12. 

To find the square root of any number without using a calculator we have to check whether the number is first a perfect square or not. For a number that is perfectly square, we can find the square root using the prime factorization method and for those that end with a first odd number, the square root can be found using repeated subtraction.

Since 12 is not a perfect square number we follow long division to find the square root of 12. 

Prime factorization

Since there are no prime factors for 12 because they are even numbers the factors of 12 are considered
The factors of 12 =  2×2×3
Since there is no square root let us take the square root on both sides
√12 = √ 22×√ 3
= 2×√ 3
√ 12 =2 ×1.732
12 = 3.46

Steps to find the square root of 12

  • Step 1: Find the smallest integer that can divide the number. The smallest integer is closest and can be divided using the number 3.
  • Step 2: Keep following the long division using divisor and dividend.
Long division method
Long division method
  • Step 3: When the particular number of satisfaction is reached the quotient is the square root of the number.  Hence, the √12 = 3.464

Solved examples

Q1: Find the square root of 12 using the prime factorization method.
A1: The factors of 12 =  2×2×3
Since there is no square root let us take the square root on both sides
√12 = √ 22×√ 3
= 2×√ 3
√ 12 =2 ×1.732
12 = 3.46

Q2: Dareen has to find the square root of 12 using the long division method, help him.

Long division method

A2: 12 = 3.464

Q3: Find the square root of 1.
A3: The square root of 1 is 1

Q4: Find the square root of -1.
A4: The square root of -1 = i

Q5: what is the square root of 169?
A5: 169 = 13 × 13
√169 = 132
Hence, √169 = 13

Frequently asked questions

What is the √12?
√12 =  3.464

Which method is used to find the 12?
The standard method that is used to find the square root of any number is the long division method.

How to write the square root of 12 in exponential form? 
121/2 or 120.5 is the exponential way to write √12

How to write the square root of 12 in radical form?
The radical form of writing square root is √12

Can I find the square root of 12 using other methods?
Prime factorization and long division are the two methods used to find the square root of 12. Repeated subtraction is not used because that is not a perfect square number.

Is 12  an irrational number?
Yes, 12 is an irrational number since the number is not equal to zero.

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

We hope that we have answered all your queries regarding the square root of 12!

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Prerit Jain

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