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.
Table of Contents
- √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
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.