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Square Root

What Is the Square Root of 2? | How to Find the Square Root of 2?

Written by Prerit Jain

Updated on: 12 Aug 2023

What Is the Square Root of 2? | How to Find the Square Root of 2?

What Is the Square Root of 2? | How to Find the Square Root of 2?

The square root of 2 is 1.4142135623730951 mentioned with a symbol √. The square root of 2 is denoted using √2.

The square root of a number is determined when a quantity of a number is produced when multiplied by itself or a factor of a number when multiplied by itself gives the original number. In simple terms when a value is multiplied by itself it gives the original number. For a better understanding. The number 2 when multiplied by itself (2×2) = 4. The square root for √2 is 1.414.

Calculation for the Square Root of 2

To find the square root of any number first the given number is usually checked to determine whether they are a perfect square number or not. The square of the number s is found using the long division method. For the number with a perfect square, it is easy to find the square roots and it is a bit tough for non-square values. Numbers like 4,9, 16,25, etc., are perfect squares. Numbers that end with 2,3,7 and 8 are not perfect square numbers.

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

These methods described above do not apply to finding the square root of any number.  

Steps to find the square root of 2

  • Step 1: Find the smallest integer that can divide the number. 
  • Step 2: Keep following the long division using divisor and dividend. 
  • Step 3: When the particular number of satisfaction is reached the quotient is the square root of the number.

Long division method

  • Step 1: Find the smallest integer that can divide the number. 
    • 1 is the perfect root number that is smaller and closest to 2.
  • 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 √2 = 1.4142

Solved examples

Q1: Find the square root of 4 using the prime factorization method
A1: Prime factors of 4 = 2×2
The √4 = 2

Q2: What is the square root of 2?

Long division method 
Long division method 

The √2 = 1.4142

Q3: What is the square root of 49 using repeated division
A3: 49-1 = 48
48-3 = 45
45-5 = 40
40-7 = 33
33-9 = 24
24-11 = 13
13-13 = 0
The √49 = 7.

Q 4: What is the square root of 3
A4: Since 3 is not a perfect square number the long division method is used to find the square root of 3.
The square root of 3 = 1.7320

Q5: What is the square root of 5
A5: The square root of 5 is
√5 = 2.2360

Frequently asked question

What are the √2?
The √2 = 1.4142

Which method is used to find the √2
The standard method that is used to find the square root of any number is the long division method.

How to write square root in exponential form? 
21/2 or 20.5 is the exponential way to write √2

How to write square root in radical form?
The radical form of writing square root is √2

Can I find the square root of 2 using other methods?
The other two methods are not applicable as 2 is not a perfect square number.

Is 2 an irrational number?
Yes, 2 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
1. Prime factorization method
2. Long division method
3. Repeated subtraction

We hope that we have answered all your queries related to the square root of 2!

Written by

Prerit Jain

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