Square Root of 8

Square root of 8 is 2.82842712475. Square root of a number, when multiplied by itself results in the original number. The radical version of the square root of 8 is represented as √8. Even in exponential form, it can be written as (8)^1/2 or (8)^0.5.

In this article, we will learn the methods to find the square root of 8 in detail.

What is Square Root of 8?

Square root of 8, is denoted by √8. Thus, the square root symbol √ can be used to denote any square root. The value of √8 is approximately 2.828. When 2.828 is multiplied twice, or 2.828 x 2.828, the result is 8. The approximate numerical value of √8 is given below

Radical Form: √8 = 2.82842712475

OR

Exponential Form: (8)^1/2 = 2.82842712475

For practical purposes, it is often rounded to a few decimal places, such as 2.82

Square Root Calculator

Try the following calculator to find the value of Square root of 8:

Methods to Find Square Root of 8

Some of the methods to find out the square root of 8 are given below:

• Square Root 8 Value by Long Division Method
• Square Root 8 Value by Prime Factorization

Let us understand these methods one by one.

Square Root of 8 by Long Division Method

We can find the square root of 8 by using the long division method using the following steps:

• First write the number 8 in decimal form, i.e. 8.000000
• Then, Start pairing the digits from right to left.
• Select a number (Divisor = 2) whose square is less than or equal to the 8. Divide it and write the quotient which is 2 and the remainder is 4.
• Write down the next pair to the right side of the pair which is 00.
• Now add the divisor with the quotient which is 2 + 2 = 4, and write down by leaving some space on the right side.
• Next, we select a new digit (which is 8) and write next to the new divisor which is 4 to find the number whose multiplication is less than or equal to the dividend which is 400.
• Now we get the number 8 as 48 8 = 364, which is less than 400.
• Continue, the process until we find the complete square root of 8.

Below is the pictorial representation of finding square root of 8 with this method:

👁 square-root-of-8

Read More, Square Root by Long Division Method

Square Root of 8 by Prime Factorization

To find the square root of 8 by prime factorisation method we must first express the number 8 as a product of its prime components to determine the value of √8. So, let's see the breakdown of numbers in the following steps:

• Now by Prime Factorization we have, 8 = 2³, that is 2 x 2 x 2.
• Therefore, √8 = √2³ or √2 x √2 x √2 
• Then, it gives √8 = 2 x √2 [As √2 x √2 = 2]
• Hence, we can write √8 = 2√2
• Now, we know that √2= 1.41421...
• Therefore, √8 = 2 x 1.41421.. = 2.82842..

Is Square Root 8 Rational or Irrational?

Square root of 8 is an irrational number. In the case of √8, the decimal expansion is non terminating and non repeating. This decimal expansion cannot be written in the form of p/q. Hence √8 is an Irrational number. Furthermore, the square root of 8 is also expressed as 2√2, √2 being an irrational number, proves that √8 is also an irrational number. As the product of a rational and irrational number is always irrational.

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