How to Find Square Root of 8?
Some of the methods to find out the square root of 8 are given below:
- Root 8 Value by Long Division Method
- 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 this method:
Read More, Square Root by Long Division Method
Square Root of 8 by Prime Factorization
We must first express the number 8 as a product of its prime components to determine the value of β8. So, letβs 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, β8 = β23 or β2 x β2 x β2
- Then, it gives β8 = 2 x β2 [As β2 x β2 = 2]
- Hence, we can write β8 = 2β2
- Now, we know that β2= 1.41421β¦
- Therefore, β8 = 2 x 1.41421.. = 2.82842..
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 β8. 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.
Contact Us