Square Root of 8
Did you know that 8 is not a perfect square? Let's learn how to calculate the square root of 8 using the long division method. We will also go through some solved examples and interactive questions in this mini lesson. Let us now see what the square root of 8 is.
 Square Root of 8: √8 = 2.82842
 Square of 8: 8^{2} = 64
What Is the Square Root of 8?
We know that addition has an inverse operation as subtraction and multiplication has an inverse operation as division. Similarly, finding the square root is an inverse operation of squaring a number. The square root of 8 gives a number that when multiplied to itself gives the number 8. Hence, we have to think of a number whose square is 8.
Is the Square Root of 8 Rational or Irrational?
A rational number is a number that can be expressed in the form of p/q, where p and q are integers and q is not equal to 0. A number that is not a rational number is called an irrational number. Nonterminating decimals that have repeated numbers after the decimal point are rational numbers. Now let us look at the square root of 8. The decimal representation of √8 is 2.828427125
Do you think the decimal part stops after 2.828427125?
No, it is neverending. It is a nonterminating decimal with nonrepeating digits. The number 2.828427125... can't be written in p/q form.
Hence, the square root of 8 is not a rational number. It is an irrational number.
How to Find the Square Root of 8?
We will discuss two methods to find the square root of 8.
 Simplifying the radical of the numbers that are perfect squares
 Long division method for perfect and nonperfect squares
The prime factorization of 8 is 8 = 2 × 2 × 2. Therefore, √8 can be simplified further as √8 =√(2 × 2 × 2) = 2√2. Thus, we have expressed the square root of 8 in the simplest radical form as 2√2
So, √8 = 2√2
Square Root of 8 by Long Division Method
The value of the square root of 8 by long division method consists of the following steps:
 Step 1: Starting from the right, we will pair up the digits by putting a bar above them.
 Step 2: Find a number that, when multiplied to itself, gives the product less than or equal to 8. So, the number is 2. Keeping the divisor as 2, we get the quotient as 2 and the remainder as 4.
 Step 3: Double the divisor and enter it with a blank on its right. Guess the largest possible digit to fill in the blank which will become the new digit in the quotient, such that when the new divisor is multiplied to the new quotient the resultant product is less than or equal to the dividend. Divide and write the remainder. Repeat this process to get the decimal places you want.
Can you use this method to find the square root of 7?
Explore square roots using illustrations and interactive examples
Important Notes:
 Square root is the inverse operation of squaring.
 Square root of 8 can be expressed as √8 = 8^{1/2}.
 We can find the square root of 8 using the radical form and the long division method.
Think Tank:
 We know that (2√2) × (2√2) = 8. So, can we say that 2√2 is a square root of 8?
 Can you determine a quadratic equation whose roots are 2√2 and 2√2?
Square Root of 8 Solved Examples

Example 1: Mr. Smith wants to fence his square garden. The garden has an area of 8 square feet. How long is each side of the garden?
Solution
To find the side of the square garden, we will have to find the square root of 8. The square root of 8 is √8 = 2√2. Hence, the side length of the garden is 2√2 feet.
Example 2: Lucy is doing yoga in her yard. The gate in her yard has an area of 12 square feet. What is the height of the gate?

Example 2: Lucy is doing yoga in her yard. The gate in her yard has an area of 12 square feet. What is the height of the gate?
Solution
By finding the square root of the area of the gate, we can find the side length of the gate.
Using the property of square roots, we have √12 = √3 × √4 = √3 × 2 = 2√3
Hence, the side length of the gate is 2√3 feet.
FAQs on Square Root of 8
What is the square root of 8?
The square root of 8 is 2√2.
Does 8 have a square root?
Yes, 8 has a square root as 2√2.
How do you find the square root of 8?
We can find the square root of 8 by using the prime factorization and long division methods.
How do you simplify square roots?
We have to express the number as the product of primes. To find the square root of the number, we should take one number from each pair of the same numbers and multiply them. For example, √100 = √(2 × 2 × 5 × 5) = 2 × 5 = 10
Is square root of 8 a real number?
Yes, square root of 8 is a real number.
What is the square root of 8 in simplified form?
The square root of 8 in simplified form is 2√2.