What Is the Square Root of 6? How To Find the Square Root of 6?

The square root of 6 is 2.44. 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 6. 

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Method to find the square root of 6

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 6 is not a perfect square number we follow long division to find the square root of 6. 

Prime factorization method

The prime factors of 6 =  2×3

Since there is no square root let us take the square root on both sides
√6 = √2*√3
= √2*√3
√6 = 1.414*1.732
√6 = 2.44

Long division method

• Step 1: Find the smallest integer that can divide the number. 
  • The smallest integer is closest and can be divided using the number 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 √6 = 2.44

Solved Example

Example 1: Find the square root of 6 using the prime factorization method
The prime factors of 6 =  2×3
Since there is no square root let us take the square root on both sides
√6 = √2*√3
√6 = 1.414*1.732
√6 = 2.44

Example 4: Find the square root of 100.
The square root of 100 is √100 = 10

Example 5: what is the square root of 169?
169 = 13 × 13
169 = 13²
Hence, the square root of 169 is √169 = 13

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Frequently asked questions

What is the √6?
√6 =  4.22

Which method is used to find the √6?
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 6 in exponential form? 
(6^1/2 )or 6^0.5 is the exponential way to write 6

How to write the square root of 6 in radical form?
The radical form of writing square root is 6

Can I find the square root of 6 using other methods?
Finding the square root for 6 is not possible using the prime factorization method or repeated subtraction because 6 is not a perfect square number.

Is 6  an irrational number?
Yes, 6 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