Square Root

# What Is the Square Root of 3? How to Find the Square Root of 3?

Written by Prerit Jain

Updated on: 05 Aug 2024

Contents

### What Is the Square Root of 3? How to Find the Square Root of 3?

The square root of 3 is 1.732. 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 3 is a positive real number that when multiplied by itself produces the number 3. The square root of 3 is mentioned as √3.

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 3 is not a perfect square number we follow long division to find the square root of 3.

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**Steps to find the square root of 3**

**Step 1:**Find the smallest integer that can divide the number. The smallest integer is closest and can be divided using the number 1.**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**square root of 3 is 1.732**

**Solved examples**

**Q 1: Find the square root of 3.**

**A 1: **Hence, the √3 = 1.732

**Q 2: What is the square root of 5?**

**A 2: **√5 = 2.23

**Q 3: Find the square root of 2.**

**A 3: **√2** **= 1.4142

**Q 4: Find the square root of 36.**

A4: The prime factors of 36 = 2² × 3²

√36 = 2× 3

Hence, √36 = 6

**Q 5: What is the square root of 64?**

The prime factors of 64 = 2×2×2×2×2×2

The common square factors = 2×2×2 = 8.

Hence, 64 = 8.

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**Frequently asked questions**

**What is the square root of 3?**

√3 = 1.732

**Which method is used to find the square root of 3?**

The common method that is used to find the square root of any number is the long division method.

**How to write the square root of 3 in exponential form?**

312 or 3^{0.5 }is the exponential way to write √3.

**How to write the square root of 3 in radical form?**

The radical form of writing square root is √3.

**Can I find the square root of 3 using other methods?**

Finding the square root for 3 is not possible using the prime factorization method or repeated subtraction because √3** **is not a perfect square number.

**Is 3 an irrational number?**

Yes, 3 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

Written by by

Prerit Jain