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.

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Square Root of 4: 2Square Root of 4 in exponential form: (4)½ or (4)0.5Square Root of 4 in radical form: √4
1.What Is the Square Root of 4?
2.IsSquare Root of 4Rational or Irrational?
3.How to Find the Square Root of 4?
4.FAQs on Square Root of 4

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

Consider the example:

22= 2× 2is 4

Here 2is called the square root of 4. 4 is a perfect square. So the square root of 4is 2. Non-square numbers also have a square root, just that they are notwhole numbers.For real numbers aand b,

a2= ba=√bThis means that ais the 2nd root ofb.

The square root of 4in the radical form is expressed as√4and inexponentform, it is expressed as 4½The square root of 4 is the inverse operation of squaring 2 and -2

2 × 2 = 4(-2)× (-2) = 4

Is the Square Root of 4Rational orIrrational?


A number that can be expressed as a ratio of twointegers, i.e., p/q, q = 0 is called arational number.Now let us look at the square root of 4.√4= 2 = 2/1Thus, √4is 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 4using prime factorization:

4 = 2× 2√4 = √22√4 = (22)½By 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 4by the long division method!

Square Root of 4ByLong Division

Let us follow the steps to find the square root of 4by 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 asinside 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 that2× 2 is 4and is equal to 4. Now let us divide 4by 2

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

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Explore Square roots using illustrations and interactive examples


Challenging Questions:


Evaluate the following:3√2 + 7√2 + 10√24√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 4is expressed as 4½The real roots ofx2- 4 = 0 are±2.