# Square root of 4

Note that 4 is a composite even number. If a square has an area of 4 unit2, 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.

#### Important Things:

• √4 = 2
• 4 is a perfect square.
• 41/2 is the exponential form of square root of 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=22

Taking square root on both sides, we get that

√4 = √22

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

√4 = (22)1/2

= 21/2   as we know that (am)n = am×n

= 2= 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.