Square Root

# What Is the Square Root of 12? | How to Find the Square Root of 12?

Written by Prerit Jain

Updated on: 12 Aug 2023

Contents

### What Is the Square Root of 12? | How to Find the Square Root of 12?

The square root of 12 is 3.464. 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 12.

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 12 is not a perfect square number we follow long division to find the square root of 12.

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**Prime factorization**

Since there are no prime factors for 12 because they are even numbers the factors of 12 are considered

The factors of 12 = 2×2×3

Since there is no square root let us take the square root on both sides

√12 = √ 2^{2}×√ 3

= 2×√ 3

√ 12 =2 ×1.732

√**12 = 3.46**

**Steps to find the square root of 12**

**Step 1:**Find the smallest integer that can divide the number. The smallest integer is closest and can be divided using the number 3.

**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 √12 = 3.464

**Solved examples**

**Q1: Find the square root of 12 using the prime factorization method**.

A1: The factors of 12 = 2×2×3

Since there is no square root let us take the square root on both sides

√12 = √ 2^{2}×√ 3

= 2×√ 3

√ 12 =2 ×1.732

√**12 = 3.46**

**Q2: Dareen has to find the square root of 12 using the long division method, help him**.

A2: **√**12 = 3.464

**Q3: Find the square root of 1.**

A3: The square root of 1 is 1

**Q4: Find the square root of -1.**

A4: The square root of -1 = i

**Q5: what is the square root of 169?**

A5: 169 = 13 × 13

√169 = 13^{2}

Hence, √**169 = 13**

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**Frequently asked questions**

**What is the √12?**

√12 = 3.464

**Which method is used to find the 12?**

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 12 in exponential form?**

12^{1/2} or 12^{0.5 }is the exponential way to write √**12**

**How to write the square root of 12 in radical form?**

The radical form of writing square root i**s √12**

**Can I find the square root of 12 using other methods?**

Prime factorization and long division are the two methods used to find the square root of 12. Repeated subtraction is not used because that is not a perfect square number.

**Is 12 an irrational number?**

Yes, 12 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

Prime factorization method

Long division method

Repeated subtraction

We hope that we have answered all your queries regarding the square root of 12!

Written by

Prerit Jain