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

Table of Contents

**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.