Square Root of 4 - How to Find the Square Root of 4? - Cuemath (2024)

The square root of 4 is expressed as √4 in the radical form and as (4)^½ or (4)^0.5 in the exponent form. It is the positive solution of the equation x² = 4.

• Square Root of 4: 2
• Square Root of 4 in exponential form: (4)^½ or (4)^0.5
• Square Root of 4 in radical form: √4

What Is the Square Root of 4?

Let us first understand the meaning of square root. The square root of a number is the number that, when multiplied to itself, gives the product as the original number.

Consider the example:

• 2² = 2 × 2 is 4

Here 2 is called the square root of 4. 4 is a perfect square. So the square root of 4 is 2. Non-square numbers also have a square root, just that they are not whole numbers.
For real numbers a and b,

• a² = b
• a=√b
• This means that a is the 2nd root of b.

The square root of 4 in the radical form is expressed as √4 and in exponent form, it is expressed as 4^½
The square root of 4 is the inverse operation of squaring 2 and -2

• 2 × 2 = 4
• (-2) × (-2) = 4

Is the Square Root of 4 Rational or Irrational?

A number that can be expressed as a ratio of two integers, i.e., p/q, q = 0 is called a rational number.
Now let us look at the square root of 4.
√4 = 2 = 2/1
Thus, √4 is a rational number.

How to Find the Square Root of 4?

There are different ways to calculate the square root of 4. The first method is by prime factorization and the second is the conventional long division method.

Prime Factorization

Let us find the square root of 4 using prime factorization:

• 4 = 2 × 2
• √4 = √2²
• √4 = (2²)^½
• By the law of exponents, considering the powers alone, 2 × ½ = 1.
• (2²)^½ = 2
• √4 = 2

Let us now try finding the square root of 4 by the long division method!

Square Root of 4 By Long Division

Let us follow the steps to find the square root of 4 by long division.

• Step 1: Group the digits into pairs (for digits to the left of the decimal point, pair them from right to left) by placing a bar over it. Since our number is 4, let us represent it as inside the division symbol.
• Step 2: Find the largest number such that when you multiply it with itself, the product is less than or equal to 4. We know that 2 × 2 is 4 and is equal to 4. Now let us divide 4 by 2

Thus the complete process of the long division stops here as the remainder is 0. Thus, the quotient 2 is the square root of 4.

Explore Square roots using illustrations and interactive examples

• Square Root of 2
• Square Root of 11
• Square Root of 5
• Square Root of 10
• Square Root of 8

Challenging Questions:

• Evaluate the following:
  3√2 + 7√2 + 10√2
  4√4 + 5√4 - 10√25

Important Notes:

• The square root of 4 in the radical form is expressed as √4.
• In exponent form, the square root of 4 is expressed as 4^½
• The real roots of x² - 4 = 0 are ±2.

FAQs on the Square Root of 4

What is the Value of the Square Root of 4?

The square root of 4 is 2.

Why is the Square Root of 4 a Rational Number?

Upon prime factorizing 4 i.e. 2², the power is in even power. Therefore, the square root of 4 is rational.

What is the Value of 16 square root 4?

The square root of 4 is 2. Therefore, 16 √4 = 16 × 2 = 32.

If the Square Root of 4 is 2. Find the Value of the Square Root of 0.04.

Let us represent √0.04 in p/q form i.e. √(4/100) = 2/10 = 0.2. Hence, the value of √0.04 = 0.2

What is the Square Root of 4 in Simplest Radical Form?

We need to express 4 as the product of its prime factors i.e. 4 = 2 × 2. Therefore, as visible, the radical form of the square root of 4 cannot be simplified further. Therefore, the simplest radical form of the square root of 4 can be written as √4

Is the number 4 a Perfect Square?

The prime factorization of 4 = 2². Here, all the prime factors are in the pair. Therefore, 4 is a perfect square.