Square root of 4

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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.

• Basic concepts of square roots

• Properties of square roots

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

= 22×1/2   as we know that (am)n = am×n

= 21 = 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.
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