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Square Root

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

Written by Prerit Jain

Updated on: 17 Aug 2023

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

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. 

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.
square root of 3
Long division method
  • 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

square root of 3

Q 2: What is the square root of 5?

Long Division Method

A 2: √5 = 2.23

Q 3: Find the square root of 2.

Long Division Method

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.

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 30.5 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

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Prerit Jain

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