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Square Root

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

Written by Prerit Jain

Updated on: 12 Aug 2023

### 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.

## 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 2: Sonu has to find the square root of 6 using the long division method, help him

√6 = 2.44

Example 3: Find the square root of 2.

The square root of 2 is √2 = 1.4142

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

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?
(61/2 )or 60.5 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

Written by by

Prerit Jain

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