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.

Looking to Learn Math? Explore Wiingy’s Online Math Tutoring Services to learn from top mathematicians and experts.

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.

• 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?

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

Looking to Learn Math? Explore Wiingy’s Online Math Tutoring Services to learn from top mathematicians and experts.

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? 
2^1/2 or 2^0.5 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!