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Square Root

What Is The Square Root of 4? How To Find The Square Root of 4?

Written by Prerit Jain

Updated on: 17 Aug 2023

What Is The Square Root of 4? How To Find The Square Root of 4?

What Is The Square Root of 4? How To Find The Square Root of 4?

The square root of 4 is 2. The inversion of subtraction is addition, and the inversion of multiplication is division in the same way the inversion of the square root of a value is squaring the number. The value of any number that when multiplied by itself gives the original number. The number 2 when they are squared 22 gives 4, and when the number is multiplied by itself 2*2 it gives the original value 4. 

For any given number before finding its square root, we must know whether the given number is a perfect square number or not. A perfect square number is one that when squared has a whole number and was easy to find. A non-perfect square number when squared has only integers and not a whole number and is found using the long division method. 

Method to find the square root of 4

  • Prime factorization method
  • Repeated subtraction method
  • Long division method

Prime factorization method

Prime factorization is one of the easiest methods to find the square root of any number. Let us take n as the prime number, by grouping the similar numbers together we get n2, by multiplying the similar n2. The value we get is the square root of the number. 

The prime factor of 4 = 2*2
By squaring them we get 22, since two is the only similar square we take the common one.
Here, the common square is 2.
Hence, the √4 = 2

Repeated subtraction method

For the repeated subtraction method we should start to multiply the given number with only odd numbers. The step in which zero is obtained is the square root of the given number.

4 – 1 = 3
3 – 3 = 0
Here, the value zero is obtained in the second step.
Hence, the √4 = 2

Long division method

The divisor for the perfect square is easy to find. The number when multiplied twice should give the value of the original number. In this case 2 when multiplied gives 4. Hence 2 is used as a divisor.

Hence, the √4 = 2

Solved examples

Example 1: What is the sum of the square of 4 and the square root of 4?
Square of 4= 16
The square root of 4 = 2
The sum of the square of 4 and the square root of 4 = 16+2 = 18

Example 2: Joe wants to find the square root value of 81/9 help him solve the sum
The 9 = 3.
The 81 = 9
Therefore, the 4/81 = 2/9.

Example 3: Solve 44 + 24
The 4 = 2.
Hence 4 (2) + 2 (2).
= 8+4
=12.

Example 4: what is the area of the square whose each side is equal to 2cm
Area of the square = x2
Here x= 2
Therefore, 22 = 2 2 = 4
Hence the area of the square with 2cm = 4 sq. cm

Frequently asked questions

What is the square root of 4?
The square root of 4 = 2.

Explain why the square root of 4 is a rational number.
When finding the prime factor of 4 we get 22 which is entirely an even power and hence all the numbers are positive integers which makes them rational numbers.

What is the value of 4 and the square root of 4?
The square root of 4 is 2, therefore 44 = 4*2 = 8

What is the real value for the square root of 4?
The actual value for the 4 = 2

What is the square root of 25?
The square root of 25 = 5

What is the square root of (-4)?
The square root of minus digits is imaginary numbers or imaginary units which really don’t have a square root.

Is 4 a perfect square number?
Yes, 4 is a perfect square number.

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Prerit Jain

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