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.

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#### Important Things:

- √8 = 2.828
- 8 is not a perfect square.
- 8
^{1/2}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.

**More about 8:**

**•** As 8=2^{3}, we can write 8=p^{3} for some prime number p. Note that p=2 here.

**• **As 8 is a multiple of 2, it is an even number.

**•** The value of the square root of 8 is 2.828.

- Cube root of 8: The value of the cube root of 8 is 2.
- Factors of 8 : The factors of 8 are 1, 2, 4, and 8.

**Also read: **Divisors of 8

This article is written by Dr. T. Mandal, Ph.D in Mathematics. On Mathstoon.com you will find Maths from very basic level to advanced level. Thanks for visiting.