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

Contents

### 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 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 = 13^{2}

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 i**s 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

Prerit Jain