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 of 8 Calculator
Try the following calculator to find the value of Square root of 8:
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 √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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Square Root of 8 – Frequently Asked Questions
What is the Value of Square Root 8?
The square root of 8 is approximately equal to 2.82.
What is Square of 8?
The square of 8 is represented by the symbol 82, and its calculation is 82 = 8 × 8 = 64. Therefore, the square of 8 is equal to 64.
What is Cube Root of 8?
The cube root of 8 , ∛8 = 2.
Is the Number 8 a Perfect Square?
No, 8 is not a perfect square because it cannot be expressed as the product of two equal integers.
Why is Square Root of 8 an Irrational Number?
Similar to non-perfect square numbers, √8 is irrational as it cannot be expressed as a ratio of two integers.
Is -2.828 a Square Root of 8?
Yes, -2.828 is a square root of 8 because -2.828 × -2.828 = 7.9524 which is approximately equal to 8.