What Is the Square Root of 8? How Do You Find the Square Root of 8?

The square root of 8 is 2.828. The inversion operation of addition is subtraction and the same goes for multiplication and division. Understanding a square root is as simple as that. The inversion of the square root value is squaring the given number. The square root of the number is the value when multiplied by itself gives the original number. 

For the number that are perfectly square, there are three ways to find them for the numbers that are not square use of the long division is the standard way to find them. When a number is given, a square root must be found. First, we have to check whether the number is a perfect square or not or you can also check if the number is an irrational number or not.

To know whether the number is rational or irrational. Let us take two numbers p and q if [p/q does not equal 0], then the number is a rational number. If the two numbers p and q when divided equally to 0 then the given number is an irrational number p/q = 0.

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How to find the square root of 8

• Step 1: Find the nearest integer that can divide the number. [The nearest integer that can divide 8 is 2]
• Step 2: Divide the numbers until you reach a satisfactory digit after the decimal

• Step 3: The quotient is the square root of the number
  • √8 = 2.828

Solved examples

Example 1: Find the square root of 36 using the repeated subtraction method.

1. 36-1 = 35
2. 35-3 = 32
3. 32-5 = 27
4. 27-7 = 20
5. 20-9 = 11
6. 11-11 = 0

A1: √36 = 6

Example 2: What is the square root of 8?

A2: √8 = 2.828

Example 3: Lucky is playing in his yard. The gate in his yard is 12 square feet. Find the height of the gate. 

If we find the square root area of the gate then we can easily find the height of the gate,
Use the knowledge of square root to find the solution,
√12 = √3 * √4
√12 = √3 * 2 =  2√3
The side length of the gate = 2√3 feet.

Example 4: What is the square root of 16?
A3: √16 = 2*2*2*2
The square root of 16 = 4

Example 5: What is the square root of 3?

A4: √3 = 1.732

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Frequently asked questions

Which is the standard method to find the square root of an irrational number?
The standard method to find the square root of an irrational number is the long division method.

What is the square root of 8?
The √8 = 2.828

How to write the square root of 8 in exponential form? 
(8^1/2 )or (8)^0.5 is the exponential way to write √8

How to write the square root of 8 in radical form?
The radical form of writing square root is √8

Can I find the square root of 3 using other methods?
Finding the square root for 8 is not possible using the prime factorization method or repeated subtraction because √8 is not a perfect square number.

Is √8  an irrational number?
Yes, 8 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