Note that 4 is a composite even number. If a square has an area of 4 unit^{2}, then we use the value of the square root of 4 to find the length of the square. We denote the square root of 4 by the symbol √4. Note that The value of the square root of 4 is 2. If you want to know more about square root, visit the following pages.

• Basic concepts of square roots

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**Important Things:**

**√4 = 2****4**is a perfect square.**4**is the exponential form of square root of^{1/2}**4**.**√4**is the radical form of square root of**4**.- The square root of
**4**is**2.000**in decimal form. - Square of
**4: 4×4 = 16**

Let us now calculate the square root of 4.

**What is Square Root of 4?**

The square root of 4 is 2. To prove this, we will write 4 as a square of some numbers.

Note that 4=2×2.

As 4 is a product of two number of 2‘s, we can write

4=2^{2}

Taking square root on both sides, we get that

√4 = √2^{2}

As square root can be written as power 1/2, we have

√4 = (2^{2})^{1/2}

= 2^{2×}^{1/2} as we know that (a^{m})^{n }= a^{m×n}

= 2^{1 }= 2

So the value of the square root of 4 is 2.

**Is 4 a perfect square number?**

We have calculated above that √4=2. As 2 is a whole number so we get that the square root of 4 is a whole number. Thus by the definition of a perfect square, we conclude that 4 is a perfect square number.

**Square root of 4 by Prime Factorization**

To find the square root of 4 by the prime factorization method, we will factorize the number 4.

Note that 4 is an even number. Thus 2 will divide it and we get

4 = 2×2 …(∗)

As 2 is a prime number, we will stop factorizing further. So (∗) is the prime factorization of 4.

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

√4 = √2×2 = 2 as we know that √a×a=a

∴ the square root of 4 is 2.

**Is Square Root of 4 Rational?**

We know that every rational number can be expressed as p/q where p and q are integers and q is non-zero.

From above we have √4=2. Note that 2=2/1. So 2 is a rational number. This implies that the square root of 4 is also a rational number. Conclusion: √4 is not an irrational number.

#### Key Things about 4

- The number 4 is the smallest positive composite number. Its proper divisors are 1 and 2.
- A number is divisible by 4 if the last two digits of that number is divisible by 4. For example, 1024 is divisible by 4 as its last two digits 24 is divisible by 4.

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.