# Square root of 8

The square root of 8 is a number when we multiply by itself, it will be 8, and we denote it by the symbol √8. Before we start computing the square root of 8, let us note down few interesting facts about the number 8.

#### Important Things:

• √8 = 2.828
• 8 is not a perfect square.
• 81/2 is the exponential form of square root of 8.
• √8 is the radical form of square root of 8.
• The square root of 8 is 2.828 corrected up to 3 decimal places.
• Square of 8: 8×8 = 64
• √8 is a quadratic surd.
• The simplified form of √8 is 2√2.

Let us now calculate the square root of 8.

#### Simplify square root of 8

What is the square root of 8 in simplest radical form? Note that 8=4×2. Here 4 is a perfect square number whose square root is 2. Taking square root on both sides of 8 = 4×2, we get that

√8 = √(4×2)

= √4 × √2  as we know that √(a×b)=√a×√b.

= 2 × √2   as √4=2.

= 2√2

So we have that:

 The simplest form of the square root of 8 is 2√2.

#### What is the value of root 8?

From above we get that the square root of 8 is 2√2. We know that √2=1.414, we deduce that

√8 = 2√2 = 2 × 1.414 = 2.828

So we obtain that:

 The value of the square root of 8 is 2.828

#### Square root of 8 by Prime Factorization

We will now find the square root of 8 by the prime factorization method. At first, we will factorize the number 8.

As 8 is an even number, it will be divisible by 2. Thus we write

8=2×4.

We all know that 4=2×2, so we obtain that

8=2×4=2×2×2 …(∗)

As 2 is a prime number, the above is the prime factorization of 8.

Taking square root on both sides of (∗), we get that

√8 = √(2×2×2)

= √(2×2) × √2

= 2 × √2   as √(a×a)=a.

= 2√2

2√2 is the square root of 8.

#### Is Square root of 8 Rational?

We have computed that √8=2√2. It is known to us that √2 is an irrational number. This implies that the square root of 8 is also an irrational number. In other words, √8 is not a rational number.

Conclusion: √8 is not a rational number.

#### Is 8 a perfect square?

As √8=2√2, we observe that the square root of 8 is not a natural number. Thus, the number 8 is not a perfect square number. Thus, 8 is a non-perfect square number. So its square root, that is, √8 is a quadratic surd.