Square root of 8 – value and examples

The square root of 8 in radical form is denoted by √8. The value of root 8 is an irrational number. Its value up to 4 decimal places is 2.828. The square root is a concept that equates to the undoing of the square operation, and on squaring 2.828 we are going to get a value that is almost equal to 8.

Let us first look at the concept of exponents with respect to the square root operation. For example, if we have a number ‘a’ and multiply it with itself ‘n’ number of times, then aⁿ = a x a x a ….. n times

Here, we know that we must multiply the number by itself to get its square value. Therefore, ‘n’ = 2.

Now, let ‘a’ be 4

Then, 4² = 4 x 4 = 16. 

16 is the square of 4, and upon inversing the square operation, we know that 4 is the square root of 16. 

This article will tell us more about finding the square root of 8 and why it is an irrational number. 

How to find the square root of 8?

We can find the square root of 8 by using any one of the methods given below:

• By prime factorization 
• By long division 

Prime factorization method

In this method, we first find the factors of 8

8 = 2 x 2 x 2 

So, √8 can be written as √(2 x 2 x 2)

( we make pairs of equal factors and pick up one factor from each pair)

Now, √8 = 2√2

We know √2 = 1.414. 

√8 = 2 x 1.414 = 2.828

Long division method

• We can find the square root of 8 by first adding zeros to the right of the decimal. 
• We know that the square of 2 is 4 and the square of 3 is 9, so we will take the number with a square less than 8 and place it as a divisor.
• Take the number 2, as the new divisor and quotient and 8 as the dividend. Then we  divide it with  the next remaining number below the extreme left.
• Bring down the next pair of numbers to the right of the remainder under the next bar.
• To calculate the divisor, multiply the previous quotient by 2 and choose a number that is less than or equal to the new dividend.
• By repeating the above steps until we get zero remainder, we can find the square root of 8 by the long division method.

Root 8 is an irrational number

Let us look at the value of root 8, √8 = 2.82842712474619……

The numbers after the decimal are non-terminating and non-repeating, and we cannot write the value of √8 in the form of p/q (where p and q are integers and q not equal to 0). Hence, the value of root 8 is irrational. It would have been rational if the digits after the decimal place were terminating or repetitive.